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Renormalization group

In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum  and resolution distance scales being effectively conjugate under the uncertainty principle.

A change in scale is called a scale transformation. The renormalization group is intimately related to scale invariance and conformal invariance, symmetries in which a system appears the same at all scales (self-similarity).

As the scale varies, it is as if one is changing the magnifying power of a notional microscope viewing the system. In so-called renormalizable theories, the system at one scale will generally consist of self-similar copies of itself when viewed at a smaller scale, with different parameters describing the components of the system. The components, or fundamental variables, may relate to atoms, elementary particles, atomic spins, etc. The parameters of the theory typically describe the interactions of the components. These may be variable couplings which measure the strength of various forces, or mass parameters themselves. The components themselves may appear to be composed of more of the self-same components as one goes to shorter distances.

For example, in quantum electrodynamics (QED), an electron appears to be composed of electron and positron pairs and photons, as one views it at higher resolution, at very short distances. The electron at such short distances has a slightly different electric charge than does the dressed electron seen at large distances, and this change, or running, in the value of the electric charge is determined by the renormalization group equation.

History
The idea of scale transformations and scale invariance is old in physics: Scaling arguments were commonplace for the Pythagorean school, Euclid, and up to Galileo. They became popular again at the end of the 19th century, perhaps the first example being the idea of enhanced viscosity of Osborne Reynolds, as a way to explain turbulence.

The renormalization group was initially devised in particle physics, but nowadays its applications extend to solid-state physics, fluid mechanics, physical cosmology, and even nanotechnology. An early article by Ernst Stueckelberg and André Petermann in 1953 anticipates the idea in quantum field theory. Stueckelberg and Petermann opened the field conceptually. They noted that renormalization exhibits a group of transformations which transfer quantities from the bare terms to the counter terms. They introduced a function h(e) in quantum electrodynamics (QED), which is now called the beta function (see below).

Beginnings
Murray Gell-Mann and Francis E. Low restricted the idea to scale transformations in QED in 1954, which are the most physically significant, and focused on asymptotic forms of the photon propagator at high energies. They determined the variation of the electromagnetic coupling in QED, by appreciating the simplicity of the scaling structure of that theory. They thus discovered that the coupling parameter g(μ) at the energy scale μ is effectively given by the (one-dimensional translation) group equation
 * $$g(\mu)=G^{-1}\left(\left(\frac{\mu}{M}\right)^d G(g(M))\right)$$

or equivalently, $$G\left(g(\mu)\right)= G(g(M))\left({\mu}/{M}\right)^d$$, for some function G (unspecified—nowadays called Wegner's scaling function) and a constant d, in terms of the coupling g(M) at a reference scale M.

Gell-Mann and Low realized in these results that the effective scale can be arbitrarily taken as μ, and can vary to define the theory at any other scale:
 * $$g(\kappa)=G^{-1}\left(\left(\frac{\kappa}{\mu}\right)^d G(g(\mu))\right) = G^{-1}\left(\left(\frac{\kappa}{M}\right)^d G(g(M))\right)$$

The gist of the RG is this group property: as the scale μ varies, the theory presents a self-similar replica of itself, and any scale can be accessed similarly from any other scale, by group action, a formal transitive conjugacy of couplings in the mathematical sense (Schröder's equation).

On the basis of this (finite) group equation and its scaling property, Gell-Mann and Low could then focus on infinitesimal transformations, and invented a computational method based on a mathematical flow function $ψ(g) = G d/(∂G/∂g)$ of the coupling parameter g, which they introduced. Like the function h(e) of Stueckelberg and Petermann, their function determines the differential change of the coupling g(μ) with respect to a small change in energy scale μ through a differential equation, the renormalization group equation:
 * $$ \displaystyle\frac{\partial g}{\partial \ln\mu} = \psi(g) = \beta(g) $$

The modern name is also indicated, the beta function, introduced by C. Callan and K. Symanzik in 1970. Since it is a mere function of g, integration in g of a perturbative estimate of it permits specification of the renormalization trajectory of the coupling, that is, its variation with energy, effectively the function G in this perturbative approximation. The renormalization group prediction (cf. Stueckelberg–Petermann and Gell-Mann–Low works) was confirmed 40 years later at the LEP accelerator experiments: the fine structure "constant" of QED was measured to be about $1/127$ at energies close to 200 GeV, as opposed to the standard low-energy physics value of $1/137$.

Deeper understanding
The renormalization group emerges from the renormalization of the quantum field variables, which normally has to address the problem of infinities in a quantum field theory. This problem of systematically handling the infinities of quantum field theory to obtain finite physical quantities was solved for QED by Richard Feynman, Julian Schwinger and Shin'ichirō Tomonaga, who received the 1965 Nobel prize for these contributions. They effectively devised the theory of mass and charge renormalization, in which the infinity in the momentum scale is cut off by an ultra-large regulator, Λ.

The dependence of physical quantities, such as the electric charge or electron mass, on the scale Λ is hidden, effectively swapped for the longer-distance scales at which the physical quantities are measured, and, as a result, all observable quantities end up being finite instead, even for an infinite Λ. Gell-Mann and Low thus realized in these results that, infinitesimally, while a tiny change in  g is provided by the above RG equation given ψ(g), the self-similarity is expressed by the fact that ψ(g) depends explicitly only upon the parameter(s) of the theory, and not upon the scale μ. Consequently, the above renormalization group equation may be solved for (G and thus) g(μ).

A deeper understanding of the physical meaning and generalization of the renormalization process, which goes beyond the dilation group of conventional renormalizable theories, considers methods where widely different scales of lengths appear simultaneously. It came from condensed matter physics: Leo P. Kadanoff's paper in 1966 proposed the "block-spin" renormalization group. The "blocking idea" is a way to define the components of the theory at large distances as aggregates of components at shorter distances.

This approach covered the conceptual point and was given full computational substance in the extensive important contributions of Kenneth Wilson. The power of Wilson's ideas was demonstrated by a constructive iterative renormalization solution of a long-standing problem, the Kondo problem, in 1975, as well as the preceding seminal developments of his new method in the theory of second-order phase transitions and critical phenomena in 1971. He was awarded the Nobel prize for these decisive contributions in 1982.

Reformulation
Meanwhile, the RG in particle physics had been reformulated in more practical terms by Callan and Symanzik in 1970. The above beta function, which describes the "running of the coupling" parameter with scale, was also found to amount to the "canonical trace anomaly", which represents the quantum-mechanical breaking of scale (dilation) symmetry in a field theory. Applications of the RG to particle physics exploded in number in the 1970s with the establishment of the Standard Model.

In 1973, it was discovered that a theory of interacting colored quarks, called quantum chromodynamics, had a negative beta function. This means that an initial high-energy value of the coupling will eventuate a special value of $μ$ at which the coupling blows up (diverges). This special value is the scale of the strong interactions, $μ$ = $Λ$$QCD$ and occurs at about 200 MeV. Conversely, the coupling becomes weak at very high energies (asymptotic freedom), and the quarks become observable as point-like particles, in deep inelastic scattering, as anticipated by Feynman–Bjorken scaling. QCD was thereby established as the quantum field theory controlling the strong interactions of particles.

Momentum space RG also became a highly developed tool in solid state physics, but was hindered by the extensive use of perturbation theory, which prevented the theory from succeeding in strongly correlated systems.

Conformal symmetry
Conformal symmetry is associated with the vanishing of the beta function. This can occur naturally if a coupling constant is attracted, by running, toward a fixed point at which β(g) = 0. In QCD, the fixed point occurs at short distances where g → 0 and is called a (trivial) ultraviolet fixed point. For heavy quarks, such as the top quark, the coupling to the mass-giving Higgs boson runs toward a fixed non-zero (non-trivial) infrared fixed point, first predicted by Pendleton and Ross (1981), and C. T. Hill. The top quark Yukawa coupling lies slightly below the infrared fixed point of the Standard Model suggesting the possibility of additional new physics, such as sequential heavy Higgs bosons.

In string theory, conformal invariance of the string world-sheet is a fundamental symmetry: β = 0 is a requirement. Here, β is a function of the geometry of the space-time in which the string moves. This determines the space-time dimensionality of the string theory and enforces Einstein's equations of general relativity on the geometry. The RG is of fundamental importance to string theory and theories of grand unification.

It is also the modern key idea underlying critical phenomena in condensed matter physics. Indeed, the RG has become one of the most important tools of modern physics. It is often used in combination with the Monte Carlo method.

Block spin
This section introduces pedagogically a picture of RG which may be easiest to grasp: the block spin RG, devised by Leo P. Kadanoff in 1966.

Consider a 2D solid, a set of atoms in a perfect square array, as depicted in the figure.

Assume that atoms interact among themselves only with their nearest neighbours, and that the system is at a given temperature $T$. The strength of their interaction is quantified by a certain coupling $J$. The physics of the system will be described by a certain formula, say the Hamiltonian $H(T, J)$.

Now proceed to divide the solid into blocks of 2×2 squares; we attempt to describe the system in terms of block variables, i.e., variables which describe the average behavior of the block. Further assume that, by some lucky coincidence, the physics of block variables is described by a formula of the same kind, but with different values for $T$ and $J$ : $H(T, J)$. (This isn't exactly true, in general, but it is often a good first approximation.)

Perhaps, the initial problem was too hard to solve, since there were too many atoms. Now, in the renormalized problem we have only one fourth of them. But why stop now? Another iteration of the same kind leads to $H(T",J")$, and only one sixteenth of the atoms. We are increasing the observation scale with each RG step.

Of course, the best idea is to iterate until there is only one very big block. Since the number of atoms in any real sample of material is very large, this is more or less equivalent to finding the long range behaviour of the RG transformation which took $(T,J) → (T,J)$ and $(T, J) → (T", J")$. Often, when iterated many times, this RG transformation leads to a certain number of fixed points.

To be more concrete, consider a magnetic system (e.g., the Ising model), in which the $J$ coupling denotes the trend of neighbour spins to be parallel. The configuration of the system is the result of the tradeoff between the ordering $J$ term and the disordering effect of temperature.

For many models of this kind there are three fixed points:
 * 1) $T = 0$ and $J → ∞$. This means that, at the largest size, temperature becomes unimportant, i.e., the disordering factor vanishes. Thus, in large scales, the system appears to be ordered. We are in a ferromagnetic phase.
 * 2) $T → ∞$ and $J → 0$. Exactly the opposite; here, temperature dominates, and the system is disordered at large scales.
 * 3) A nontrivial point between them, $T = T_{c}$ and $J = J_{c}$. In this point, changing the scale does not change the physics, because the system is in a fractal state. It corresponds to the Curie phase transition, and is also called a critical point.

So, if we are given a certain material with given values of $T$ and $J$, all we have to do in order to find out the large-scale behaviour of the system is to iterate the pair until we find the corresponding fixed point.

Elementary theory
In more technical terms, let us assume that we have a theory described by a certain function $$Z$$ of the state variables $$\{s_i\}$$ and a certain set of coupling constants $$\{J_k\}$$. This function may be a partition function, an action, a Hamiltonian, etc. It must contain the whole description of the physics of the system.

Now we consider a certain blocking transformation of the state variables $$\{s_i\}\to \{\tilde s_i\}$$, the number of $$\tilde s_i$$ must be lower than the number of $$s_i$$. Now let us try to rewrite the $$Z$$ function only in terms of the $$\tilde s_i$$. If this is achievable by a certain change in the parameters, $$\{J_k\}\to \{\tilde J_k\}$$, then the theory is said to be renormalizable.

Most fundamental theories of physics such as quantum electrodynamics, quantum chromodynamics and electro-weak interaction, but not gravity, are exactly renormalizable. Also, most theories in condensed matter physics are approximately renormalizable, from superconductivity to fluid turbulence.

The change in the parameters is implemented by a certain beta function: $$\{\tilde J_k\}=\beta(\{ J_k \})$$, which is said to induce a renormalization group flow (or RG flow) on the $$J$$-space. The values of $$J$$ under the flow are called running couplings.

As was stated in the previous section, the most important information in the RG flow are its fixed points. The possible macroscopic states of the system, at a large scale, are given by this set of fixed points. If these fixed points correspond to a free field theory, the theory is said to exhibit quantum triviality, possessing what is called a Landau pole, as in quantum electrodynamics. For a $φ$4 interaction, Michael Aizenman proved that this theory is indeed trivial, for space-time dimension $D$ ≥ 5. For $4 d$ = 4, the triviality has yet to be proven rigorously, but lattice computations have provided strong evidence for this. This fact is important as quantum triviality can be used to bound or even predict parameters such as the Higgs boson mass in asymptotic safety scenarios. Numerous fixed points appear in the study of lattice Higgs theories, but the nature of the quantum field theories associated with these remains an open question.

Since the RG transformations in such systems are lossy (i.e.: the number of variables decreases - see as an example in a different context, Lossy data compression), there need not be an inverse for a given RG transformation. Thus, in such lossy systems, the renormalization group is, in fact, a semigroup, as lossiness implies that there is no unique inverse for each element.

Relevant and irrelevant operators and universality classes
Consider a certain observable $D$ of a physical system undergoing an RG transformation. The magnitude of the observable as the length scale of the system goes from small to large determines the importance of the observable(s) for the scaling law: A relevant observable is needed to describe the macroscopic behaviour of the system; irrelevant observables are not needed. Marginal observables may or may not need to be taken into account. A remarkable broad fact is that most observables are irrelevant, i.e., the macroscopic physics is dominated by only a few observables in most systems.

As an example, in microscopic physics, to describe a system consisting of a mole of carbon-12 atoms we need of the order of 10$A$ (the Avogadro number) variables, while to describe it as a macroscopic system (12 grams of carbon-12) we only need a few.

Before Wilson's RG approach, there was an astonishing empirical fact to explain: The coincidence of the critical exponents (i.e., the exponents of the reduced-temperature dependence of several quantities near a second order phase transition) in very disparate phenomena, such as magnetic systems, superfluid transition (Lambda transition), alloy physics, etc. So in general, thermodynamic features of a system near a phase transition depend only on a small number of variables, such as the dimensionality and symmetry, but are insensitive to details of the underlying microscopic properties of the system.

This coincidence of critical exponents for ostensibly quite different physical systems, called universality, is easily explained using the renormalization group, by demonstrating that the differences in phenomena among the individual fine-scale components are determined by irrelevant observables, while the relevant observables are shared in common. Hence many macroscopic phenomena may be grouped into a small set of universality classes, specified by the shared sets of relevant observables.

Momentum space
Renormalization groups, in practice, come in two main "flavors". The Kadanoff picture explained above refers mainly to the so-called real-space RG.

Momentum-space RG on the other hand, has a longer history despite its relative subtlety. It can be used for systems where the degrees of freedom can be cast in terms of the Fourier modes of a given field. The RG transformation proceeds by integrating out a certain set of high-momentum (large-wavenumber) modes. Since large wavenumbers are related to short-length scales, the momentum-space RG results in an essentially analogous coarse-graining effect as with real-space RG.

Momentum-space RG is usually performed on a perturbation expansion. The validity of such an expansion is predicated upon the actual physics of a system being close to that of a free field system. In this case, one may calculate observables by summing the leading terms in the expansion. This approach has proved successful for many theories, including most of particle physics, but fails for systems whose physics is very far from any free system, i.e., systems with strong correlations.

As an example of the physical meaning of RG in particle physics, consider an overview of charge renormalization in quantum electrodynamics (QED). Suppose we have a point positive charge of a certain true (or bare) magnitude. The electromagnetic field around it has a certain energy, and thus may produce some virtual electron-positron pairs (for example). Although virtual particles annihilate very quickly, during their short lives the electron will be attracted by the charge, and the positron will be repelled. Since this happens uniformly everywhere near the point charge, where its electric field is sufficiently strong, these pairs effectively create a screen around the charge when viewed from far away. The measured strength of the charge will depend on how close our measuring probe can approach the point charge, bypassing more of the screen of virtual particles the closer it gets. Hence a dependence of a certain coupling constant (here, the electric charge) with distance scale.

Momentum and length scales are related inversely, according to the de Broglie relation: The higher the energy or momentum scale we may reach, the lower the length scale we may probe and resolve. Therefore, the momentum-space RG practitioners sometimes claim to integrate out high momenta or high energy from their theories.

Exact renormalization group equations
An exact renormalization group equation (ERGE) is one that takes irrelevant couplings into account. There are several formulations.

The Wilson ERGE is the simplest conceptually, but is practically impossible to implement. Fourier transform into momentum space after Wick rotating into Euclidean space. Insist upon a hard momentum cutoff, $p^{2} ≤ Λ^{2}$ so that the only degrees of freedom are those with momenta less than $23$. The partition function is
 * $$Z=\int_{p^2\leq \Lambda^2} \mathcal{D}\phi \exp\left[-S_\Lambda[\phi]\right].$$

For any positive $Λ$ less than  $Λ'$, define $S_{Λ'}$ (a functional over field configurations  $Λ$ whose Fourier transform has momentum support within $p^{2} ≤ Λ' ^{2}$) as
 * $$\exp\left(-S_{\Lambda'}[\phi]\right)\ \stackrel{\mathrm{def}}{=}\ \int_{\Lambda'  \leq p \leq \Lambda} \mathcal{D}\phi   \exp\left[-S_\Lambda[\phi]\right].$$

If $S_{Λ}$ depends only on $φ$ and not on derivatives of $ϕ$, this may be rewritten as

$$\exp\left(-S_{\Lambda'}[\phi]\right)\ \stackrel{\mathrm{def}}{=}\ \prod_{\Lambda'  \leq p \leq \Lambda}\int d\phi(p)   \exp\left[-S_\Lambda[\phi(p)]\right],$$

in which it becomes clear that, since only functions $ϕ$ with support between $ϕ$  and  $Λ'$ are integrated over, the left hand side may still depend on $ϕ$ with support outside that range. Obviously,
 * $$Z=\int_{p^2\leq {\Lambda'}^2}\mathcal{D}\phi \exp\left[-S_{\Lambda'}[\phi]\right].$$

In fact, this transformation is transitive. If you compute $S_{Λ'}$ from  $S_{Λ}$ and then compute $S_{Λ'}$ from $S_{Λ'}$, this gives you the same Wilsonian action as computing SΛ″ directly from SΛ.

The Polchinski ERGE involves a smooth UV regulator cutoff. Basically, the idea is an improvement over the Wilson ERGE. Instead of a sharp momentum cutoff, it uses a smooth cutoff. Essentially, we suppress contributions from momenta greater than $Λ$ heavily. The smoothness of the cutoff, however, allows us to derive a functional differential equation in the cutoff scale $Λ$. As in Wilson's approach, we have a different action functional for each cutoff energy scale $Λ$. Each of these actions are supposed to describe exactly the same model which means that their partition functionals have to match exactly.

In other words, (for a real scalar field; generalizations to other fields are obvious),
 * $$Z_\Lambda[J]=\int \mathcal{D}\phi \exp\left(-S_\Lambda[\phi]+J\cdot \phi\right)=\int \mathcal{D}\phi \exp\left(-\tfrac{1}{2}\phi\cdot R_\Lambda \cdot \phi-S_{\text{int}\,\Lambda}[\phi]+J\cdot\phi\right)$$

and ZΛ is really independent of $Λ$! We have used the condensed deWitt notation here. We have also split the bare action SΛ into a quadratic kinetic part and an interacting part Sint Λ. This split most certainly isn't clean. The "interacting" part can very well also contain quadratic kinetic terms. In fact, if there is any wave function renormalization, it most certainly will. This can be somewhat reduced by introducing field rescalings. RΛ is a function of the momentum p and the second term in the exponent is
 * $$\frac{1}{2}\int \frac{d^dp}{(2\pi)^d}\tilde{\phi}^*(p)R_\Lambda(p)\tilde{\phi}(p)$$

when expanded.

When $$p \ll \Lambda$$, $R_{Λ}(p)/p^{2}$ is essentially 1. When $$p \gg \Lambda$$, $R_{Λ}(p)/p^{2}$ becomes very very huge and approaches infinity. $R_{Λ}(p)/p^{2}$ is always greater than or equal to 1 and is smooth. Basically, this leaves the fluctuations with momenta less than the cutoff $Λ$ unaffected but heavily suppresses contributions from fluctuations with momenta greater than the cutoff. This is obviously a huge improvement over Wilson.

The condition that
 * $$\frac{d}{d\Lambda}Z_\Lambda=0$$

can be satisfied by (but not only by)
 * $$\frac{d}{d\Lambda}S_{\text{int}\,\Lambda}=\frac{1}{2}\frac{\delta S_{\text{int}\,\Lambda}}{\delta \phi}\cdot \left(\frac{d}{d\Lambda}R_\Lambda^{-1}\right)\cdot \frac{\delta S_{\text{int}\,\Lambda}}{\delta \phi}-\frac{1}{2}\operatorname{Tr}\left[\frac{\delta^2 S_{\text{int}\,\Lambda}}{\delta \phi\, \delta \phi}\cdot R_\Lambda^{-1}\right].$$

Jacques Distler claimed without proof that this ERGE is not correct nonperturbatively.

The effective average action ERGE involves a smooth IR regulator cutoff. The idea is to take all fluctuations right up to an IR scale $Λ$ into account. The effective average action will be accurate for fluctuations with momenta larger than $k$. As the parameter $k$ is lowered, the effective average action approaches the effective action which includes all quantum and classical fluctuations. In contrast, for large $k$ the effective average action is close to the "bare action". So, the effective average action interpolates between the "bare action" and the effective action.

For a real scalar field, one adds an IR cutoff
 * $$\frac{1}{2}\int \frac{d^dp}{(2\pi)^d} \tilde{\phi}^*(p)R_k(p)\tilde{\phi}(p)$$

to the action $k$, where Rk is a function of both  $S$ and  $k$ such that for $$p \gg k$$, Rk(p) is very tiny and approaches 0 and for $$p \ll k$$, $$R_k(p)\gtrsim k^2$$. Rk is both smooth and nonnegative. Its large value for small momenta leads to a suppression of their contribution to the partition function which is effectively the same thing as neglecting large-scale fluctuations.

One can use the condensed deWitt notation
 * $$\frac{1}{2} \phi\cdot R_k \cdot \phi$$

for this IR regulator.

So,
 * $$\exp\left(W_k[J]\right)=Z_k[J]=\int \mathcal{D}\phi \exp\left(-S[\phi]-\frac{1}{2}\phi \cdot R_k \cdot \phi +J\cdot\phi\right)$$

where $p$ is the source field. The Legendre transform of Wk ordinarily gives the effective action. However, the action that we started off with is really S[φ]+1/2 φ⋅Rk⋅φ and so, to get the effective average action, we subtract off 1/2 φ⋅Rk⋅φ. In other words,
 * $$\phi[J;k]=\frac{\delta W_k}{\delta J}[J]$$

can be inverted to give Jk[φ] and we define the effective average action Γk as
 * $$\Gamma_k[\phi]\ \stackrel{\mathrm{def}}{=}\ \left(-W\left[J_k[\phi]\right]+J_k[\phi]\cdot\phi\right)-\tfrac{1}{2}\phi\cdot R_k\cdot \phi.$$

Hence,
 * $$\begin{align}

\frac{d}{dk}\Gamma_k[\phi] &=-\frac{d}{dk}W_k[J_k[\phi]]-\frac{\delta W_k}{\delta J}\cdot\frac{d}{dk}J_k[\phi]+\frac{d}{dk}J_k[\phi]\cdot \phi-\tfrac{1}{2}\phi\cdot \frac{d}{dk}R_k \cdot \phi \\ &=-\frac{d}{dk}W_k[J_k[\phi]]-\tfrac{1}{2}\phi\cdot \frac{d}{dk}R_k \cdot \phi \\ &=\tfrac{1}{2}\left\langle\phi \cdot \frac{d}{dk}R_k \cdot \phi\right\rangle_{J_k[\phi];k}-\tfrac{1}{2}\phi\cdot \frac{d}{dk}R_k \cdot \phi \\ &=\tfrac{1}{2}\operatorname{Tr}\left[\left(\frac{\delta J_k}{\delta \phi}\right)^{-1}\cdot\frac{d}{dk}R_k\right] \\ &=\tfrac{1}{2}\operatorname{Tr}\left[\left(\frac{\delta^2 \Gamma_k}{\delta \phi \delta \phi}+R_k\right)^{-1}\cdot\frac{d}{dk}R_k\right] \end{align}$$

thus
 * $$\frac{d}{dk}\Gamma_k[\phi] =\tfrac{1}{2}\operatorname{Tr}\left[\left(\frac{\delta^2 \Gamma_k}{\delta \phi \delta \phi}+R_k\right)^{-1}\cdot\frac{d}{dk}R_k\right]$$

is the ERGE which is also known as the Wetterich equation. As shown by Morris the effective action Γk is in fact simply related to Polchinski's effective action Sint via a Legendre transform relation.

As there are infinitely many choices of $J$k, there are also infinitely many different interpolating ERGEs. Generalization to other fields like spinorial fields is straightforward.

Although the Polchinski ERGE and the effective average action ERGE look similar, they are based upon very different philosophies. In the effective average action ERGE, the bare action is left unchanged (and the UV cutoff scale—if there is one—is also left unchanged) but the IR contributions to the effective action are suppressed whereas in the Polchinski ERGE, the QFT is fixed once and for all but the "bare action" is varied at different energy scales to reproduce the prespecified model. Polchinski's version is certainly much closer to Wilson's idea in spirit. Note that one uses "bare actions" whereas the other uses effective (average) actions.

Renormalization group improvement of the effective potential
The renormalization group can also be used to compute effective potentials at orders higher than 1-loop. This kind of approach is particularly interesting to compute corrections to the Coleman–Weinberg mechanism. To do so, one must write the renormalization group equation in terms of the effective potential. To the case of the $$\phi^4$$ model:

 * $$\left(\mu\frac{\partial}{\partial\mu} + \beta_\lambda\frac{\partial}{\partial\lambda} + \phi\gamma_\phi\frac{\partial}{\partial\phi}\right) V_\text{eff} = 0.$$

In order to determine the effective potential, it is useful to write $$V_\text{eff}$$ as

 * $$V_\text{eff} = \frac{1}{4} \phi^4 S_\text{eff}\big(\lambda, L(\phi)\big),$$

where $$S_\text{eff}$$ is a power series in $$L(\phi) = \log \frac{\phi^2}{\mu^2}$$:

 * $$S_\text{eff} = A + BL + CL^2 + DL^3 + \dots.$$

Using the above ansatz, it is possible to solve the renormalization group equation perturbatively and find the effective potential up to desired order. A pedagogical explanation of this technique is shown in reference.

Pedagogical and historical reviews

 * The most successful variational RG method.
 * A mathematical introduction and historical overview with a stress on group theory and the application in high-energy physics.
 * A pedestrian introduction to renormalization and the renormalization group.
 * A pedestrian introduction to the renormalization group as applied in condensed matter physics.
 * A pedestrian introduction to the renormalization group as applied in condensed matter physics.

Books

 * T. D. Lee; Particle physics and introduction to field theory, Harwood academic publishers, 1981, ISBN 3-7186-0033-1. Contains a Concise, simple, and trenchant summary of the group structure, in whose discovery he was also involved, as acknowledged in Gell-Mann and Low's paper.
 * L. Ts. Adzhemyan, N. V. Antonov and A. N. Vasiliev; The Field Theoretic Renormalization Group in Fully Developed Turbulence; Gordon and Breach, 1999. ISBN 90-5699-145-0.
 * Vasil'ev, A. N.; The field theoretic renormalization group in critical behavior theory and stochastic dynamics; Chapman & Hall/CRC, 2004. ISBN 9780415310024 (Self-contained treatment of renormalization group applications with complete computations);
 * Zinn-Justin, Jean (2002). Quantum field theory and critical phenomena, Oxford, Clarendon Press (2002), ISBN 0-19-850923-5 (an exceptionally solid and thorough treatise on both topics);
 * Zinn-Justin, Jean: Renormalization and renormalization group: From the discovery of UV divergences to the concept of effective field theories, in: de Witt-Morette C., Zuber J.-B. (eds), Proceedings of the NATO ASI on Quantum Field Theory: Perspective and Prospective, June 15–26, 1998, Les Houches, France, Kluwer Academic Publishers, NATO ASI Series C 530, 375-388 (1999) [ISBN ]. Full text available in PostScript.
 * Kleinert, H. and Schulte Frohlinde, V; Critical Properties of $R$4-Theories, World Scientific (Singapore, 2001); Paperback ISBN 981-02-4658-7''. Full text available in PDF.

title: Renormalization group


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Britney (album)

Britney is the third studio album by American singer Britney Spears. It was released on October 31, 2001, by Jive Records.

Looking to transition from the teen pop styles of her first two studio albums ...Baby One More Time (1999) and Oops!... I Did It Again (2000), Spears began to embrace a significantly more mature sound with Britney. The record incorporates genres of pop and R&B with influences of EDM and occasionally dips into disco, hip hop, rock, and electronica. Its lyrical themes address the subjects such as coming of age, adulthood, control, and sexuality. Contributions to its production came from a variety of collaborators, including Max Martin and Rami Yacoub. Spears herself assumed a more prominent role in the album's development, co-writing six of its tracks.

Britney received generally mixed reviews from music critics, who complimented Spears' musical progression but criticized her increasingly provocative image. Regardless, the album was a global commercial success and debuted atop the US Billboard 200 with first-week sales of 746,000 copies, making Spears the first female artist to have her first three studio albums debut atop the chart, a record she would later break with her fourth studio album In the Zone (2003). The album received a nomination for Best Pop Vocal Album at the 45th Annual Grammy Awards (2003). With worldwide sales of over 10 million copies, Britney is one of the best-selling albums of the 21st century.

Britney produced six singles. "I'm a Slave 4 U" reached the top ten in 20 countries but peaked only at number 27 on the US Billboard Hot 100, becoming Spears's first lead single not to peak within the top ten. "Overprotected" also achieved international commercial success but peaked only at number 86 the US Billboard Hot 100. "I'm Not a Girl, Not Yet a Woman", "I Love Rock 'n' Roll" and "Boys" reached the top ten in several countries but all failed to enter the US Billboard Hot 100, while "Anticipating" was released exclusively in France instead of "I Love Rock 'n' Roll". To further promote the album, Spears embarked on her fourth concert tour, titled Dream Within a Dream Tour, from November 2001 until July 2002.

Recording and production
For her second studio album Oops!... I Did It Again, which was released in May 2000 to global commercial success, Spears collaborated with producers such as Rodney Jerkins, Rami Yacoub, and Max Martin; all of them returned for Britney. Spears additionally worked with a variety of collaborators, including her then-boyfriend Justin Timberlake. She commented that she initially felt "awkward" and "nervous" working with Timberlake, saying that she was accustomed to the process being "like work". For the first time, Spears worked with hip hop producers the Neptunes. She claimed to have been inspired by "a lot of hip-hop and R&B while I was on my last tour. I was inspired by Jay-Z and the Neptunes. I told Jive I really wanted to work with [the Neptunes]. I wanted to make [Britney] nastier and funkier." Spears was additionally set to record songs with Missy Elliott and Timbaland, which never came to fruition due to scheduling conflicts.

While recording Britney, Spears wanted an "older generation to pick up on it", adding that she "had to change it up and pray people think that's cool". She stated that she chose to self-title the album because the majority of its content described herself. Spears recorded 23 tracks for the album, several of which she co-wrote with the assistance of Brian Kierulf and Josh Schwartz. She added that personally writing the album and developing its concept made the project "that much more special", elaborating of her intentions to "get better and grow" as a songwriter. During the sessions, Spears also worked with electronic musician BT, whose tracks were excluded from the standard edition track listing. She stated: "I was really disappointed we weren't able to use the tracks BT had done. He's a genius in whatever he does, but the type of music he ended up doing didn't fit me and what I was going for. I think they will be on some of the stuff [released] overseas." His contribution "Before the Goodbye" was included on international editions of the album.

Music and lyrics
Britney is a pop and R&B record with dance influences. It opens with the urban and Middle Eastern-influenced "I'm a Slave 4 U", which showcases breathy, emotive noises, and has been compared to "Nasty Girl" by Vanity 6. Spears commented that its lyrics are "about me just wanting to go out and forget who I am and dance and have a good time". Europop-styled "Overprotected" addresses a girl tired of being manipulated. Lyrically, "Lonely" sees a girl moving on from a troublesome romance after being lied to and manipulated, being considered "a teenage version" of Janet Jackson's "What About". The soft rock piano ballad "I'm Not a Girl, Not Yet a Woman", co-written by English singer-songwriter Dido, details the emotional struggles girls experience during puberty. "Boys" incorporates R&B and hip hop styles, and was criticized by David Browne of Entertainment Weekly as "cut-rate '80s Janet Jackson". The disco-inspired track "Anticipating" discusses the friendship and camaraderie between women, and was described as reminiscent of Madonna's "Holiday" and "Kylie in disco mood."

Spears' cover of "I Love Rock 'n' Roll", made famous by Joan Jett and the Blackhearts, infuses pop rock styles into the original hard rock rendition. "Cinderella" reflects on a female protagonist who left her boyfriend after he failed to appreciate her efforts in the relationship. "Let Me Be" sees Spears ask to be trusted as an adult and be afforded her own opinions. "Bombastic Love" discusses a love in which the protagonist feels that the romance will happen "exactly like in a movie". Similarly, "That's Where You Take Me" details the joy she gets from an emotionally fulfilling relationship, amid Middle Eastern chimes and a collage of electronic beats and drum programming. On the electronica international editions bonus track "When I Found You", Spears sings about having found the "deepest love" in her soulmate who is essentially a reflection of herself. Britney closes with "What It's Like to Be Me", which was co-written and co-produced by Spears's then-boyfriend Justin Timberlake; Spears sings that a guy must "figure [her] out" to "be [her] man".

Release and promotion
On January 28, 2001, Spears performed at Super Bowl XXXV. Shortly after, she appeared on Total Request Live to premiere new material from Britney. On September 6, Spears premiered "I'm a Slave 4 U" at the 2001 MTV Video Music Awards; the performance was criticized for her use of a yellow python as a stage prop. Four days later, she performed "I'm a Slave 4 U" on The Rosie O'Donnell Show. Spears was scheduled to perform and hold a press conference in Australia on September 13; however, she cancelled the event in light of the September 11 attacks two days prior, saying that holding the conference would have been inappropriate. The following month, Spears performed at The Tonight Show with Jay Leno.

Britney was first released in Japan on October 31, being released in the United States on November 6, by Jive Records. An accompanying video album, titled Britney: The Videos, was released two weeks later. It included a selection of her earlier music videos, behind-the-scenes footage, commercials, and notable live performances. The video peaked atop the US Top Music Videos on December 8. Spears had already begun her Dream Within a Dream Tour in Columbus, Ohio five days before Britney was released in the US; the tour ended on July 28, 2002 in Mexico City. Shortly after it began, she performed in her first HBO concert special from the MGM Grand Garden Arena in Las Vegas; Cher was supposed to join Spears onstage for the song "The Beat Goes On", which Spears covered on ...Baby One More Time, but was unable to do so due to scheduling conflicts.

On December 4, 2001, Spears performed at the 2001 Billboard Music Awards in Las Vegas. On January 9, 2002, she performed "I'm Not a Girl, Not Yet a Woman" at the 2002 American Music Awards. Later that month, Spears gave interviews to The Frank Skinner Show in the United Kingdom and The Saturday Show in Australia. Crossroads premiered in February, allowing Spears to simultaneously promote both the film and her album. On February 2, she was featured as both the host and performer on Saturday Night Live. A week later, she performed "I'm Not a Girl, Not Yet a Woman" at the NBA All-Star Game and The Tonight Show with Jay Leno. Spears also appeared on Live with Regis and Kelly, The View, and the 44th Annual Grammy Awards, as well as the German talk show Wetten, dass..?.

Singles

Britney became Spears' first album not to produce a single US Billboard Hot 100 top-ten hit. Reportedly, Clear Channel Entertainment "punished" Spears for her management not choosing them as the tour promoter for the Dream Within a Dream Tour by blacklisting her on their radio stations, which greatly affected the performance of her subsequent singles, starting with "I'm a Slave 4 U". The song was released as the album's lead single on September 25, 2001 to critical acclaim. Due to the radio blacklist, it peaked only at number 27 on the US Billboard Hot 100, becoming Spears' first lead single not to peak within the top ten. It fared better internationally, debuting at number four on the UK Singles Chart and peaking within the top ten in 20 countries. Its accompanying music video was directed by Francis Lawrence, and received three nominations at the 2002 MTV Video Music Awards.

"Overprotected" was released as the second international single from Britney on December 10, 2001, and the third North American single on April 2, 2002. Its Darkchild remix peaked at number 86 on the US Billboard Hot 100, while the original version reached the top ten in Belgium, Croatia, Finland, Greece, Hungary, Ireland, Italy, Norway, Poland, Romania, Sweden and the United Kingdom. Critically acclaimed, the song was nominated for the Best Female Pop Vocal Performance at the 45th Annual Grammy Awards (2003). Two accompanying music videos were released–the Bille Woodruff-directed video for the original version and the Chris Applebaum-directed Darkchild remix video.

Staggered to fit the varying release dates of Crossroads internationally, "I'm Not a Girl, Not Yet a Woman" was released as the film's theme song and the second North American single from Britney on January 7, 2002 to critical acclaim. It peaked at number two on the Bubbling Under Hot 100 Singles, the Billboard Hot 100 extension chart. The song fared better internationally, peaking at number two in the UK, and within the top ten in Australia, Austria, the Czech Republic, Germany, Ireland, the Netherlands and Sweden. Filmed in Arizona and at the Alstrom Point, the song's Wayne Isham-directed accompanying music video primarily consists of Spears, whilst wearing cowboy boots, performing the song whilst standing on the edge of a cliff, and inside a slot canyon.

"I Love Rock 'n' Roll" was released as the fourth international single from Britney on May 27, 2002, and the fifth and final UK single on November 4, to mixed critical reception. It reached the top ten in Austria, Croatia, Germany, Hungary, Ireland, Portugal, Scotland and Slovenia, whilst peaking at number 13 on the UK Singles Chart. Directed by Chris Applebaum, its accompanying music video shows Spears with her own band, a stack of speakers and flashing lights. In France, "Anticipating" was released as the fourth single instead of "I Love Rock 'n' Roll" on June 25; it reached number 38 on the French Singles Chart.

The Co-Ed Remix of "Boys"–featuring Pharrell Williams–was released as the fourth North American and UK single, and the fifth and final international single from Britney on June 24, 2002, also serving as the second single from the soundtrack for Austin Powers in Goldmember, to mixed critical reception. It peaked at number 22 on the US Bubbling Under Hot 100 Singles, and peaked at number seven on the UK Singles Chart. Its accompanying music video, directed by Dave Meyers, features Spears, Williams, and Mike Myers as Austin Powers at a party inside a castle, with cameo appearances from actors Jason Priestley, Justin Bruening and Taye Diggs. It was nominated for Best Video from a Film at the 2003 MTV Video Music Awards, but lost to Eminem's "Lose Yourself".

Critical reception
Britney received mixed reviews from music critics. At Metacritic, which assigns a normalized rating out of 100 to reviews from mainstream critics, Britney received an average score of 58, which indicates "mixed or average reviews", based on 13 reviews. David Browne of Entertainment Weekly found Spears's increasingly provocative image to be unnatural, noting "virginal vamping in an awkward adolescence" and "a few tentative new moves". PopMatters' Nikki Tranton complimented the production of the songs, but questioned if Spears was ready to establish herself as a grown woman in the music industry. Sal Cinquemani of Slant Magazine agreed, writing that although "Britney, [the album], fills her role of guilty pleasure (the disc certainly satiates more than the stunted growth of last year's Oops!...I Did It Again), it's time for Spears to quit being such a cock-tease and cook something up that will satisfy the ever-vacillating hype-machine."

AllMusic's Stephen Thomas Erlewine gave a positive review, feeling that the album "strives to deepen [Spears's] persona" and proves she "will know what to do when the teen-pop phenomenon of 1999–2001 passes for good". Similarly, a reviewer from Billboard commented that the project was "a nicely varied, wholly satisfying collection". Chris Heat of Dotmusic praised Britney for "us[ing] this opportunity to take the odd risk and adds a welcome edge to her sound." NME's Ted Kessler recognized the release as a "coming of age album" and joked that it "works best when making a good pop cheese and dance sandwich". By contrast, Stephen Thompson of The A.V. Club panned the album, opining that the music "just [isn't] catchy" and that "though neither a girl nor a woman, Spears inspires grown-up anger on her own". Craig Seymore of Spin recognized that she "sound[s] almost human," but criticized that "the rest of the record is as coldly anthemic as ever."

Accolades
! scope="row"| 2001 ! scope="row"| 2003
 * Billboard Music Award
 * Female Albums Artist of the Year
 * Britney Spears
 * Nominated
 * align="center"|
 * Grammy Award
 * Best Pop Vocal Album
 * Britney
 * Nominated
 * align="center"|
 * }

Commercial performance
Britney debuted at number one on the US Billboard 200 with first-week sales of 745,750 copies, which was the second highest first week sales by a female artist at the time behind Spears' own Oops!... I Did It Again which sold 1.3 million copies in its first week. In doing so, Spears became the first woman to have her first three studio albums debut atop that chart. She also held the second-highest debut album sales of 2001, behind Celebrity by NSYNC with 1.88 million units moved and was the highest debut-week sales by a female artist of the year. After fluctuating within the top 20 of the chart in the following weeks, Britney sold 3.3 million copies by March 2002. As of March 2015, Britney has sold 4.4 million units in the United States alone and was certified quadruple platinum by the Recording Industry Association of America (RIAA).

Internationally, Britney debuted atop the Canadian Albums Chart with first-week sales of 44,550 copies. It later sold 316,944 copies in the country, a significant decline in relation to the sales of ...Baby One More Time (1999) and Oops!... I Did It Again (2000). The album peaked at number four on both the Oricon Albums Chart in Japan and the UK Albums Chart. In the latter, it was certified platinum by the British Phonographic Industry (BPI) for shipments of 300,000 copies to retailers. Across the rest of Europe, Britney debuted at number one in Austria, Germany, and Switzerland. In 2002, it was certified double platinum by the International Federation of the Phonographic Industry (IFPI) for shipments of two million copies throughout Europe. The album also peaked at number four in Australia, and was certified double platinum by the Australian Recording Industry Association (ARIA). Britney was the fifth best-selling album of 2001 globally, selling seven million copies. By January 2003, the album had sold ten million copies worldwide.

Track listing
Notes
 * "I Love Rock 'n' Roll" is a cover of the 1975 Arrows single later made famous by Joan Jett & the Blackhearts in their 1982 cover of the song.
 * $undefined$ signifies a vocal producer.

Personnel
Credits are adapted from the liner notes of Britney.

 * John Amatiello – engineering (tracks 2 and 4), engineering assistance (tracks 8 and 10)
 * Dido Armstrong – songwriting (track 4)
 * James Biondolillo – string arrangement (track 6)
 * BossLady – backing vocals (tracks 2 and 10)
 * Sue Ann Carwell – backing vocals (track 7)
 * Andrew Coleman – engineering (tracks 1 and 5)
 * Tyler Collins – backing vocals (track 7)
 * Tom Coyne – mastering
 * Jaime Duncan – engineering assistance (track 12)
 * Brian Garten – engineering (track 1 and 5)
 * Stephen George – mixing (track 6)
 * Serban Ghenea – mixing (tracks 1 and 5)
 * Brad Gilderman – engineering (track 7)
 * Albert Hall – backing vocals (track 7)
 * Damion Hall – backing vocals (track 7)
 * Nana Hedin – backing vocals (track 10)
 * Jean-Marie Horvat – mixing (tracks 3, 7 and 9)
 * Rodney Jerkins – drum programming (tracks 3 and 9), production (tracks 3, 7 and 9), songwriting (track 3)
 * Richard G. Johnson – engineering assistance (track 12)
 * Jennifer Karr – backing vocals (tracks 3, 6, 9 and 11)
 * Steven Klein – photography
 * Marc Stephen Lee – engineering assistance (track 7)
 * Thomas Lindberg – bass (track 4)
 * Fabian Marasciullo – engineering (tracks 3 and 7), vocal engineering (track 9)
 * Max Martin – backing vocals (track 4), engineering (tracks 2, 4, 8 and 10), guitar (track 2), mixing (tracks 2, 4, 8 and 10), production (tracks 2, 4, 8 and 10)
 * Charles McCrorey – engineering assistance (tracks 2, 4, 6, 9 and 12)
 * Daniel Milazzo – engineering assistance (track 5)
 * Pablo Munguia – engineering (track 12)
 * The Neptunes – instruments (track 1 and 5), production (tracks 1 and 5), songwriting (tracks 1 and 5)
 * Esbjörn Öhrwall – guitar (track 4)
 * Jeanette Olsson – backing vocals (tracks 4 and 8)
 * Jeff Pescetto – backing vocals (track 7)
 * Tim Roberts – engineering assistance (tracks 1 and 5)
 * Wade Robson – production (track 12), songwriting (track 12)
 * Nile Rodgers – guitar (track 6)
 * Jason Scheff – backing vocals (track 7)
 * Ryan Smith – engineering assistance (track 1)
 * Britney Spears – conceptualization, songwriting (tracks 3, 6, 8, 9 and 11), vocals (all tracks)
 * Mark Suozzo – string arrangement (track 6)
 * Rich Tapper – engineering assistance (track 11)
 * Jill Tengan – engineering assistance (tracks 3, 6 and 9)
 * Chris Thompson – backing vocals (track 7)
 * Justin Timberlake – backing vocals (track 12), production (track 12), songwriting (track 12), vocal arrangement (track 12)
 * Michael Tucker – engineering (track 2), mixing (track 11)
 * Rami Yacoub – engineering (tracks 2, 4, 8 and 10), mixing (tracks 2, 4, 8 and 10), production (tracks 2, 4, 8 and 10), songwriting (tracks 2, 4, 8 and 10)
 * Yasu – engineering (track 6)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Britney (album)


text:
Mac 68k emulator

The Mac 68k emulator is a software emulator built into all versions of the classic Mac OS for PowerPC. This emulator enabled running applications and system code that were originally written for the 680x0-based Macintosh models. With a few exceptions, notably Connectix's RAM Doubler, the emulator ran all software with no noticeable impact other than lower performance relative to the same program when compiled for PowerPC.

Origins
The first version was written by Gary Davidian, who had originally created it for use on the Motorola 88000 CPU, used in Apple's abortive first attempt at a RISC target platform. A later version, using dynamic recompilation, was developed by Eric Traut, who later worked on successful emulation projects at Connectix such as Virtual Game Station and Virtual PC. Prior to Traut's arrival there, Connectix had released Speed Doubler, which included an even faster PowerPC 68k emulator.

Implementation
All versions of this emulator emulated the "user" subset of the 68EC040 instruction set with a 68020/68030 exception stack frame. Apple developer documents indicate that the emulator provided an operating environment most closely resembling that of the Macintosh Centris 610, a system based on the Motorola 68LC040 microprocessor. Early versions emulated it by decoding each instruction and immediately carrying out a series of equivalent PowerPC instructions. For the PCI PowerMacs, the dynamic recompilation emulator was used to boost performance. Dynamic recompilation works by "recompiling" common sections of the code into faster, PowerPC-native, sequences that were locally cached. The emulator could recognise the same sequence of 680x0 code and run the previously-cached PowerPC code to avoid doing the translation again. This emulator was theoretically capable of emulating 680x0 code faster than any real 680x0 was capable of running it. The 68LC040 had no floating point instructions, making this feat slightly simpler but no less impressive.

One reason that this emulation was so successful is that many of the APIs for the Mac OS were originally implemented as traps on the 680x0 processor; therefore, calling an API actually was recognised by the 680x0 as the equivalent of an error condition, which would cause it to handle that error through one of its hardware vectors. In turn, this vector would look up and run the operating system routine from ROM or RAM. In the emulator, such traps could be replaced by native PowerPC code, so the only code being emulated was the application itself, and any system API it called could be accelerated with native PowerPC code. This also allowed Apple time to port the OS to the PowerPC. At first only time-critical aspects were rewritten in native code, leaving much of the OS emulated. Gradually most of the OS was rewritten to be native, so the OS got faster over time.

For the programmer, the transition to the PowerPC was made fairly painless, because the emulator was started and stopped automatically. This was achieved using a new type of pointer called a Universal Procedure Pointer (UPP). For 68k code, this pointer appeared to be an ordinary pointer to code and could be used as such. However, it actually led to a data structure which contained a special trap instruction and flags indicating the instruction set architecture (ISA) of the called code. From PowerPC code, this UPP could be passed to the CallUniversalProc function to call it. The 68k emulator then dealt with details such as presenting passed parameters in the right order for the ISA in question, as well as starting and stopping the emulator as required. The compilers for Mac OS created such UPPs automatically when the proper macros were used, and the PowerPC system libraries contained native stubs to transparently call through to native or still-68k functions as needed. This meant that dealing with the dual architecture required very little work for the programmer, and just like the OS, applications themselves could mix and match 680x0 and PowerPC code fairly easily.

Current status
Because it was built into all PowerPC versions of the classic Mac OS, the emulator was also part of the Classic environment in Mac OS X. PowerPC Macintosh emulators such as SheepShaver therefore use the emulator as well when running the classic Mac OS. Native Mac OS X outside of Classic never used the emulator.

title: Mac 68k emulator


text:
Talk:Old Irish

2003 edit
The page as it exists now is inaccurate; Old Irish is no longer spoken - Old Irish is the common ancestor of Irish and Scots gaelic, but the language in use in Ireland today is most definitly "New Irish". -- Jim Regan 01:05, 8 Aug 2003 (UTC)

Plus: the article is superfluous, as it has the same subject as the Irish language page, which is more complete.Erwin 10:08, 8 Aug 2003 (UTC)

Drastically different
"Old Irish possesses much more inflection than its descendants and also employs drastically different phonetic and grammatical structures"

Yes, it is more inflectional; it depends on what you mean by 'drastically different' -both languages might still recognise each other if they met on the street, even if the modern one is 'simpler'.

However, I cannot agree with the idea of "drastically different phonetic structures". I bet natives speakers and those who can pronounce Irish, would be within an hour able to speak with the same blas as OI. In that area, it has (for older speakers, anyway) seen the least change. Apart from the dental fricatives (there were 4), one can find all other phones (/R'/ included, but that is not to say it is the same /R'/ as 1200 years ago). Given that the phonetic table only has meaning if one places phones in their appropriate boxes, and the modern langauge uses the same sounds, (apart from dental fricatives, and some alveolar r's and gemminated consonants, all of which survived into the 20th century in Donegal irish, altho the dental fricatives were in sandhi only), how can one make this spurious claim? —The preceding unsigned comment was added by 80.93.5.45 (talk • contribs)  16:30, 19 January 2006   (UTC)
 * Sorry I didn't notice this comment earlier! I agree that "drastically different" is an overstatement and have rephrased it. I do think the modern languages are phonologically much simpler than Old Irish, more in terms of overall phonotactics and syllable structure than in terms of individual phonemes. User:Angr 13:53, 6 July 2006 (UTC)

The page currently states that modern Irish had changed so much from proto-Celtic that it was not even recognized as Indo-European until the 19th century. For the sake of fairness, Indo-European studies didn't really get under way until the twilight years of the 18th century (with Jones' 1786 lecture on Sanskrit, Latin and Greek), and the term Indo-European didn't get introduced until 1813 ... the 19th century (check it). I'm willing to believe that scholars were flummoxed, but could you provide a bit more clarification/sources on where this confusion was expressed? 150.135.165.27 (talk) 23:35, 24 January 2019 (UTC)

difference
that's fair enough -I am not knowledgeable yet to comment on phonotactics

phonology
The wording: "/N/, /Nʲ/, /L/, /Lʲ/, /R/, /Rʲ/ represent fortis sonorants whose precise articulation is unknown, but which were probably longer, tenser, and generally more strongly articulated" is not very clear. "Longer", yes, that is a clear, universally understood parameter --- and about the only one clearly stated, for example, in Stifter's new book. But "tenser", "stronger" --- these are at best ad hoc terms used with different meanings by different authors for different languages. If you want to go by modern Irish as a model, then you should use precise articulatory phonetic descriptions thereof (from the literature), otherwise, it might be better not to even include such terms unless you want to say: "by stronger, I actually mean that the unlenited forms were unmarked, and that the lenited ones were approximants", or, "by tenser, I mean that laryngeal constriction accompanied the articulation", or whatever.Jakob37 13:40, 14 April 2007 (UTC)
 * Well, if we knew what the phonetic difference between the fortis and lenis consonants really was in Old Irish, I would have written that instead. Since we don't, I stuck to vague terms. Would it be better to write simply "...represent fortis sonorants whose precise articulation is unknown, but which were probably longer than their lenis counterparts, and probably differed from them somehow in articulation as well"? —Angr 13:54, 14 April 2007 (UTC)
 * One method used in historical linguistics is extrapolation: in this case, if we can fairly accurately define the modern Irish reflexes of these sounds, and if we know something about where they came from (Common Celtic and/or Indo-European), then we should be able to make a reasonable estimate of their nature in Old Irish (I haven't checked my references in the office, so this is just a general statement).Jakob37 04:48, 15 April 2007 (UTC)
 * Yes, but doing so here would be original research. We have to go by what's already been published, and AFAIK what's already been published is pretty vague on the specifics. —Angr 06:34, 15 April 2007 (UTC)

How sure are we that nasalized V actually existed?
I know this page isn't edited much but I wanted to ask. There are some phonemes that are described as being uncertain, but ṽ isn't one of them. How do we know that the supposed phonemic /ṽ/ wasn't just /v/, spelled differently simply because of its etymology? Irish has a long tradition of doing things like that, and in fact they still spell mh separately today even though the pronunciation has been merged with bh for 1000 years. Is there an Old Irish pronunciation guide somewhere, written when the language was still alive, that says that it's /ṽ/? Are there misspellings?  — Soap  —  13:04, 8 January 2011 (UTC)
 * There's good evidence it was something nasalized at any rate, because many dialects of Irish and Scottish Gaelic have nasalized vowels in position next to mh but not next to bh. It may have been a nasalized approximant like or, which is phonetically much easier to produce than a nasalized fricative, but the comparative evidence that it was somehow nasalized, and distinct from bh, is quite robust. —Angr (talk) 15:31, 8 January 2011 (UTC)
 * Addendum: while it's true Modern Irish uses relatively etymological spellings, in Old Irish, the spelling hadn't been around long enough that the pronunciation could have deviated much from it. Old Irish speakers would have had no reason to write dubae 'gloom' with b but dumae 'mound' with m if they hadn't pronounced them differently. —Angr (talk) 15:42, 8 January 2011 (UTC)
 * Thank you, that's a very helpful answer.  —  Soap  —  12:00, 9 January 2011 (UTC)
 * Isn't [m̞] a simpler, more iconic and (handily) more vague method to represent relaxed [m]? I've also seen it represented as bilabial, by the way, instead of labiodental, in transcription: [β̃]. But a non-committal notation like [m̞] allows us to avoid going into the phonetic details: labial, labiodental or even labiovelar, fricative or approximant – we can't really determine the historical pronunciation with precision anyway. Just an idea.
 * (Of course, this trick could be used to mark lenited sounds in general, i. e., fricatives or approximants as far as they have a historical relationship with less relaxed consonants. It would eliminate the need for the "Greek character solution".) --Florian Blaschke (talk) 19:05, 11 April 2012 (UTC)

Posttonic internal short vowels
According to the analysis of Old Irish phonology generally taught nowadays (which is, for example, mentioned here – in German, page 77 – and, for those who can't read German, in Stifter's textbook which the Kommentar refers to, Sengoidelc), internal short vowels following the place of the stress (the interpretation of pretonic vowels is less clear) only distinguished two values, a rounded value, usually interpreted as /u/, and an unrounded value, usually represented as schwa. Only in absolute final position, all five vowel qualities were distinguished in short vowels. Internally, the written short vowels i, e and a should absolutely not be taken as full vowels, but only as ways to represent the neutral vowel orthographically in the absence of more appropriate or specific vowel symbols. Note that from Middle Irish on, unstressed short vowels had collapsed (been neutralised) into a single vowel quality – schwa – in all positions, even in absolute final position, and the full short vowels seen in the written representation are all merely graphic. The practice to write i between slender consonants, a between broad consonants, ai between a broad and a slender consonant and e (in Modern Irish, ea) between a slender and a broad consonant, and in Modern Irish, a at the end of a word after a broad and e after a slender consonant should absolutely not be taken on face value, namely as representing true full vowels /i/, /e/ or /a/ or as diphthongs! Students of Old Irish are discouraged from this interpretation from the beginning on; it is considered a fundamental error. The practice of vowel writing in Irish is likely derived from the phonetic phenomenon that makes a central vowel between slender consonants sound /i/-coloured, between broad consonants /a/-coloured, etc., and that has phonemically irrelevant, automatic glides appear whenever a front vowel and a broad consonant or a back vowel and a slender consonant occur in sequence. In fact, the orthography (the Modern Irish spelling even slightly more so than the Old Irish system) approximates the phonetic vocalic and diphthongal qualities quite closely and nicely and is therefore easy to understand (and helpful for one's reading and pronunciation once this fact is understood). The misconception that these phonetic vowels have phonological relevance, too, however, should absolutely not be propagated in Wikipedia. Currently, the article is not at all clear on this point. The transcriptions also need adaptation. While it is OK to write [ɪ] and [ɐ] in phonetic notation, correct phonological notation may only recognise these as automatic allophones of /ə/. --Florian Blaschke (talk) 19:50, 11 April 2012 (UTC)

aspirated unvoiced stops phonetic value
Presumably /p/ /t/ /k/ in the table are phonetic [ph] etc

I think it might be worth mentioning that very briefly, for several reasons. What do you think?

CecilWard (talk) 08:50, 11 June 2014 (UTC)

 * I don't feel strongly about it one way or the other. I can't think of a reason not to mention it, but neither does it seem so important that it requires mentioning. On a different topic, do you have a source for your assertion that "In some predominant Scottish dialects these two changes [i.e. eclipsis of /p t k b d g/ to /b d g m n ŋ/] did not take place across word boundaries"? It was my understanding that morphologically conditioned eclipsis was lost in Scottish Gaelic (except for a few remnants like bheil < bhfuil), not that it never occurred there. Angr (talk) 18:42, 11 June 2014 (UTC)

Tony, Ill wirte something substantial on htese points and oost it shirtly when imget my ducks inna row, have been realky ill in recent years somthings are a bit skowCecilWard (talk) 23:46, 13 June 2014 (UTC)

Lenition and orthography
The superdot is NOT used on just f and s - it's used in manuscripts for any lenition. Ch/ph/th are modern developments. It is also used frequently on b, d, and g, depending on the manuscript. It's often left off as well. As to the nasals - it is also used irregularly, but when it is used, it indicates lenition. I have no sources at the moment (other than the standard thurneysen's grammar), but this is what I was taught as a graduate student in Old Irish. I will try to look it up this week.

"Notable Characteristics" Is possibly problematic.
https://en.wikipedia.org/wiki/Old_Irish#Notable_characteristics

This section here strikes me as wrong. I know a tiny bit of Hebrew, Ugaritic, Phoenician, etc.

A system of conjugated prepositions that is unusual in Indo-European languages (although found in many Semitic languages, e.g. Arabic), e.g. dím "from me", dít "from you", de "from him", di "from her", diib "from them" (basic preposition di "from"). There is a great deal of allomorphy here as well.

This is wrong I think. West Semitic, (Hebrew, Aramaic, Arabic, etc) uses the word Min to mean 'from.' In Hebrew, m'efo means 'from where.'

HeirOfSumer (talk) 17:24, 19 June 2015 (UTC)

Initial Consonant Mutation
The article claims: "Initial consonant mutation must have been present in at least late Common Celtic (Proto-Celtic) because this distinguishing feature has survived with grammatical significance in both modern Welsh and Breton, and the extinct Cornish language also featured. Because the languages belong to the Brittonic branch of the Celtic language group (so-called "P-Celtic"), initial mutation must predate the split in the development paths of the Brittonic and Goidelic languages. No mutations are, however, attested in Gaulish material so a parallel evolution of the phenomenon in the neo-Celtic languages is also possible. Much of the complex allomorphy has been lost, but the rich sound system has been maintained, with little change, in the modern languages."

Considering the different sound changes that brought about mutations in the two branches, isn't this a bit misleading? I find it dubious that t>th tt>t could be in parallel with t>d tt>th, as in Old Irish vs Welsh.

Source on Welsh: http://people.ds.cam.ac.uk/dwew2/old_and_middle_welsh.pdf
 * On the other hand, the lenition of /m/ to /ṽ/ is so unusual that it would be an astonishing coincidence for it to have happened separately in Goidelic and Brythonic. More likely, the lenition of /b d ɡ m/ probably happened in Proto-Insular Celtic, while the lenition of /p t k/ didn't happen until Goidelic and Brythonic had separated. —Aɴɢʀ (talk) 17:23, 12 April 2017 (UTC)
 * I agree. Seeing as mutation of /b d ɡ m/ probably occured in Proto-Celtic the phenomenon is already there to allow it to happen differently with other phonemes at a later stage. — Dyolf87 (talk) 00:20, 1 May 2021 (UTC)

"Goidelic" listed at Redirects for discussion
A discussion is taking place to address the redirect Goidelic. The discussion will occur at Redirects for discussion/Log/2020 May 31 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Soumya-8974 talk contribs subpages 06:35, 31 May 2020 (UTC)

"Goidel" listed at Redirects for discussion
A discussion is taking place to address the redirect Goidel. The discussion will occur at Redirects for discussion/Log/2020 July 3 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Soumya-8974 talk contribs subpages 17:51, 3 July 2020 (UTC)

Old Irish is accurately Old Scots Gaelic.
There is a lot of confusion regarding titles, this article should aim to interlink with factual un-bias history & corresponding wiki pages.

The exhausting issue with Wikipedia is factual history & accuracy.

The English word Irish did not exist pre-1800s, nor did Ireland, so Middle-Irish does not exist, Old Irish does not exist unless you are using the modern name to make reference only, and if those terms are to be used, then factual equivalents should be included.

When referring to Ireland in a selected period, the "correct" reference name(s) should be used for that period in time also.

From the mid 300s, and especially circa 500a.d, Ireland was named Scotia, land of Scots officially & internationally, the Scoti people or (Gaels) spoke Old Gaelic, so factually, Irish Gaelic descends from Old Gaelic or old Scots Gaelic.

Scots Gaelic if not extinct would have become modern Irish with evolution.

As we know the people were called Scots, the name for all Gaels, this accurately aligns Old Gaelic and Old Scots Gaelic, so using an accurate name would simply be Old Gaelic, Middle Gaelic, modern Irish.

If an Irish person is referring to their language, it's acceptable to use old Irish, however as I said if you say Ireland in the 1200s, then the correct name should be included.

Ireland officially ceased being called Scotia (Scotland) in the 1500s.

Rf: University of Dublin.

Old Gaelic would be acceptably neutral. 2A00:23C8:8586:9C00:B896:E401:AD36:FED4 (talk) 19:53, 3 December 2020 (UTC)DD

 * I agree that it would be better to use Primitive Gaelic, Old Gaelic, Middle Gaelic etc, however it makes no sense for Wikipedia articles to use terminology which would differ to the most widely available and popular literature - i.e. Primitive Irish, Old Irish, Middle Irish, etc because the language was spoken in what we now call Ireland. — Dyolf87 (talk) 00:14, 1 May 2021 (UTC)

 * The part about the word Irish is simply not true. The name Iryshe for the language is in use in the 16th century (see commons:File:Elizabeth_I's_primer_on_Irish.jpg), the word Gaelic is a relatively late loanword in English and gains popularity only in the 18th century (see Google ngrams). But regardless of that, as Dyolf87 pointed out, the common terminology in the literature for historical stages of the language is Old Irish and Middle Irish, and only after that Classical Gaelic and Early Modern Gaelic get used besides Classical Irish and Early Modern Irish (with Classical Gaelic typically denoting the bardic standard language used in poetry, Early Modern Irish / Early Modern Scottish Gaelic denoting the vernaculars spoken in Ireland and Scotland).

 * And the word Scots, Scottish in modern English refers exclusively to Scotland, even though Old English Scottisċ referred to the language and people of both Gaelic Ireland and Scotland. It’s not Wikipedia’s purpose to bring back the medieval meanings and uses of words. Silmethule (talk) 13:10, 14 January 2022 (UTC)
 * Agreed. Especially with the new revelations as to how Britain and Ireland were populated with Indo-Europeans during the Bronze Ages, we should be embarrassed to say the Indo-European languages came from anywhere other than the continent (unless there is strong proof to the contrary).
 * Assertions such as, “Old Irish is thus forebear to Modern Irish, Manx, and Scottish Gaelic,” should be reworked to avoid making statements that do not follow from rigorous scientific analysis. A better assertion would be, “Old Irish is the earliest recorded form of Goidelic/Insular Q-Celtic/…” Gortaleen (talk) 01:30, 28 June 2023 (UTC)

 * Old Irish is certainly still used in academia, but is there any apparent move towards Old Gaelic?. I agree that Old Gaelic is more neutral, and probably better reflects the history of Scottish Gaelic in terms of modern geography, but we need to stick to WP:COMMONNAME and avoid WP:OR.  Catfish  Jim  and the soapdish  13:30, 28 June 2023 (UTC)

 * There's nothing unscientific about calling Old Irish the precursor to ScG, IG and Manx. AFAIK Old Gaelic is not widely used, especially since it introduces and element of ambiguitiy as to whether you're talking about an older form of (say) ScG or Old Irish. There's Classical Gaelic but that's an artificial standardized form of Middle Irish which cannot taken as the precursor to ScG/Manx. It's called Old Irish because by and large our body of evidence is based on manuscripts from Ireland and because Manx and ScG don't get documented until much later, not sure why there is this fuss about neutrality on there? It's neither inaccurate nor offensive. Akerbeltz (talk) 11:38, 17 August 2023 (UTC)

They've changed Gaelic to Irish to make it (Gaelic) more foreign. They also try to ascribe every place name etymology to "Pictish" even though there is zero evidence that such a language ever existed. In short, they can't stand the fact that people in Britain/Scotland exist that don't speak English and they try to "other" those people. Gaels are "the enemy within" as it were, to be culturally eradicated from memory. They are embarrassed that the name "Scotland" derives from the Scots who spoke Gaelic. — Preceding unsigned comment added by 2A01:4B00:D004:CA00:DC2B:ADA0:63D0:87A0 (talk) 21:09, 2 July 2024 (UTC)

 * Who's "they"?
 * Pictish existed... there is no controversy there, no mainstream academic claims otherwise.
 * The claim that there are monoglot Gaelic speakers today is a stretch. Sure, some toddlers get introduced to Gaelic at home before they're exposed to English, but the last monoglot Gaelic speaker died around the 1970s.  Catfish  Jim  and the soapdish  11:39, 4 July 2024 (UTC)

Western coast of Great Britain vs Wales
you changed western coast of Great Britain to Wales in the region part of the infobox. IMO that’s wrong, the western part here denotes both parts of Wales and of Scotland. And as for Old Irish specifically – is it even attested in writing from Wales (later than the 5th–6th century ogham stones, any of them contemporary with Old Irish? ie. 7th–8th centuries?)? It surely was used in (parts of) Scotland (and attested at least in early Middle Irish manuscripts), which now isn’t in any way included in the infobox. Silmethule (talk) 13:10, 14 January 2022 (UTC)

Split History page to Phonological history of Old Irish
As the subsection heading says, content formerly in the history subsection of the article has been moved to Phonological history of Old Irish. Midnight-Blue766 (talk) 23:32, 18 August 2022 (UTC)

v/ṽ vs. β/β̃
I’m guessing  was chosen as it would be more reliably displayed in browsers with a tilde (ṽ/β̃), but isn’t it a little misleading? A mention of this being a bilabial (not labio-dental) sound would seem like a good idea. ⚜ Moilleadóir ✍ 07:14, 5 August 2023 (UTC)

Silly transcription of the mid vowels
Do we really need to write $⟨e₁ː e₂ː o₁ː o₂ː⟩$? If "it is generally thought that /e₁ː/ was higher than /e₂ː/" then surely we can just use a proper IPA transcription ⟨eː ɛː⟩ instead?! By analogy, ⟨oː ɔː⟩ can be used for their back counterparts. Sol505000 (talk) 11:15, 2 May 2024 (UTC)

title: Talk:Old Irish


text:
English Shepherd

The English Shepherd is a breed of herding dog from the United States.

Description
The English Shepherd is a medium-sized breed of dog, it weighs between 40 and 65 lb and stands between 18 and 23 in, males are typically larger than females. The breed has a long, straight or wavy double coat with feathering on the legs and tail, traditionally it has four different color combinations, black and white, black and tan, sable and white or tricolor (black, white and tan), although shades of fawn and red tan to white are also seen in the breed. According to the breed standard, the coat may be straight, wavy or curly, except on the face, skull and front of legs where it is short and smooth.

History
The progenitors of the English Shepherd were collies of various types brought to the New World by early settlers from Britain and Ireland, as such it shares ancestry with the modern Border Collie, Rough Collie and Australian Shepherd. The ancestors of the English Shepherd were used extensively on farms throughout the eastern states, principally as a sheep and cattle herder, although it also performed the roles of watchdog, ratter and companion.

The United Kennel Club (UKC) has been registering English Shepherds since 1927, originally the UKC called the breed the American Farm Shepherd but in 2003 renamed it the English Shepherd. The breed is not recognized by the American Kennel Club.

title: English Shepherd


text:
Talk:Mac 68k emulator

Untitled
Actually lots of companies have used object-code interpretation in a similar role. I know the HP used it when they moved from their HP3000 minis over to the HP-PA RISC systems for instance. IBM used it to run S/370 apps on the RT as well. In fact, I think there's about a dozen common examples of this.

User:Maury Markowitz

Where it is?
As far as I know, the emulator is included in the system ROM, as Apple documentations talks about the PowerMac ROMs saying that about between 1 and 1.5Mb are the 68k emulator while the rest are the ROM itself (that were made of OF, the emulator, and the 68k Toolbox that runs in the emulator).

When moved to NewWorld (8.5 onward) enough part of the core MacOS was PowerPC native so the emulator can be inside the system software (and was removed from ROM along with the 68k Toolbox in B&W G3 onward)

— Claunia 01:23, 26 August 2005 (UTC)

title: Talk:Mac 68k emulator


text:
Eclampsia

Eclampsia is the onset of seizures (convulsions) in a woman with pre-eclampsia. Pre-eclampsia is a hypertensive disorder of pregnancy that presents with three main features: new onset of high blood pressure, large amounts of protein in the urine or other organ dysfunction, and edema. If left untreated, pre-eclampsia can result in long-term consequences for the mother, namely increased risk of cardiovascular diseases and associated complications. In more severe cases, it may be fatal for both the mother and the fetus.

The diagnostic criterion for pre-eclampsia is high blood pressure, occurring after 20 weeks gestation or during the second half of pregnancy. Most often it occurs during the 3rd trimester of pregnancy and may occur before, during, or after delivery. The seizures are of the tonic–clonic type and typically last about a minute. Following the seizure, there is either a period of confusion or coma. Other complications include aspiration pneumonia, cerebral hemorrhage, kidney failure, pulmonary edema, HELLP syndrome, coagulopathy, placental abruption and cardiac arrest.

Low dose aspirin is recommended to prevent pre-eclampsia and eclampsia in those at high risk. Other preventative recommendations include calcium supplementation in areas with low calcium intake and treatment of prior hypertension with anti-hypertensive medications. Exercise during pregnancy may also be useful. The use of intravenous or intramuscular magnesium sulfate improves outcomes in those with severe pre-eclampsia and eclampsia and is generally safe. Treatment options include blood pressure medications such as hydralazine and emergency delivery of the baby either vaginally or by cesarean section.

Pre-eclampsia is estimated to globally affect about 5% of deliveries while eclampsia affects about 1.4% of deliveries. In the developed world eclampsia rates are about 1 in 2,000 deliveries due to improved medical care whereas in developing countries it can impact 10–30 times as many women. Hypertensive disorders of pregnancy are one of the most common causes of death in pregnancy. They resulted in 46,900 deaths in 2015. Maternal mortality due to eclampsia occurs at a rate of approximately 0–1.8% of cases in high-income countries and up to 15% of cases in low- to middle- income countries. The word eclampsia is from the Greek term for lightning. The first known description of the condition was by Hippocrates in the 5th century BC.

Signs and symptoms
Eclampsia is a disorder of pregnancy characterized by seizures in the setting of pre-eclampsia. Most women have premonitory signs/symptoms in the hours before the initial seizure. Typically the woman develops hypertension before the onset of a convulsion (seizure). Other signs and symptoms include:

Any of these symptoms may be present before or after the seizure. It is also possible for the woman to be asymptomatic prior to the onset of the seizure.
 * Long-lasting (persistent) frontal, occipital, or thunderclap headaches
 * Visual disturbance (blurred vision, photophobia, diplopopia)
 * Photophobia (discomfort from bright light)
 * Abdominal in the epigastric region (the center of the abdomen above the navel) or in the right upper quadrant of the abdomen (below the right side of the rib cage)
 * Altered mental status (confusion)

Other cerebral signs that may precede the convulsion include nausea, vomiting, headaches, and cortical blindness. If the complication of multi-organ failure ensues, signs and symptoms of those failing organs will appear, such as abdominal pain, jaundice, shortness of breath, and diminished urine output.

Onset
The seizures of eclampsia typically present during pregnancy and prior to delivery (the antepartum period), but may also occur during labor and delivery (the intrapartum period) or after the baby has been delivered (the postpartum period). If postpartum seizures develop, it is most likely to occur within the first 48 hours after delivery. However, late postpartum seizures of eclampsia may occur as late as 4 weeks after delivery.

Characteristics
Eclamptic seizure is typically described as a tonic–clonic seizure which may cause an abrupt loss of consciousness at onset. This is often associated with a shriek or scream followed by stiffness of the muscles of the arms, legs, back and chest. During the tonic phase, the mother may begin to appear cyanotic. This presentation lasts for about a minute, after which the muscles begin in jerk and twitch for an additional one to two minutes. Other signs include tongue biting, frothy and bloody sputum coming out of the mouth.

Complications
There are risks to both the mother and the fetus when eclampsia occurs. The fetus may grow more slowly than normal within the womb (uterus) of a woman with eclampsia, which is termed intrauterine growth restriction and may result in the child appearing small for gestational age or being born with low birth weight. Eclampsia may also cause problems with the placenta. The placenta may bleed (hemorrhage) or begin to separate early from the wall of the uterus. It is normal for the placenta to separate from the uterine wall during delivery, but it is abnormal for it to separate prior to delivery; this condition is called placental abruption and can be dangerous for the fetus. Placental insufficiency may also occur, a state in which the placenta fails to support appropriate fetal development because it cannot deliver the necessary amount of oxygen or nutrients to the fetus. During an eclamptic seizure, the beating of the fetal heart may become slower than normal (bradycardia). If any of these complications occurs, fetal distress may develop. Treatment of the mother's seizures may also manage fetal bradycardia. If the risk to the health of the fetus or the mother is high, the definitive treatment for eclampsia is delivery of the baby. Delivery by cesarean section may be necessary, especially if the instance of fetal bradycardia does not resolve after 10 to 15 minutes of resuscitative interventions. It may be safer to deliver the infant preterm than to wait for the full 40 weeks of fetal development to finish, and as a result prematurity is also a potential complication of eclampsia.

In the mother, changes in vision may occur as a result of eclampsia, and these changes may include blurry vision, one-sided blindness (either temporary due to amaurosis fugax or potentially permanent due to retinal detachment), or cortical blindness, which affects the vision from both eyes. There are also potential complications in the lungs. The woman may have fluid slowly collecting in the lungs in a process known as pulmonary edema. During an eclamptic seizure, it is possible for a person to vomit the contents of the stomach and to inhale some of this material in a process known as aspiration. If aspiration occurs, the woman may experience difficulty breathing immediately or could develop an infection in the lungs later, called aspiration pneumonia. It is also possible that during a seizure breathing will stop temporarily or become inefficient, and the amount of oxygen reaching the woman's body and brain will be decreased (in a state known as hypoxia). If it becomes difficult for the woman to breathe, she may need to have her breathing temporarily supported by an assistive device in a process called mechanical ventilation. In some severe eclampsia cases, the mother may become weak and sluggish (lethargy) or even comatose. These may be signs that the brain is swelling (cerebral edema) or bleeding (intracerebral hemorrhage).

Risk factors
Eclampsia, like pre-eclampsia, tends to occur more commonly in first pregnancies than subsequent pregnancies. Women who have long term high blood pressure before becoming pregnant have a greater risk of pre-eclampsia. Patients who have gestational hypertension and pre-eclampsia have an increased risk of eclampsia. Furthermore, women with other pre-existing vascular diseases (diabetes or nephropathy) or thrombophilia disease such as the antiphospholipid syndrome are at higher risk to develop pre-eclampsia and eclampsia. Having a placenta that is enlarged by multiple gestation or hydatidiform mole also increases risk of eclampsia. In addition, there is a genetic component: a woman whose mother or sister had the condition is at higher risk than otherwise. Patients who have experienced eclampsia are at increased risk for pre-eclampsia/eclampsia in a later pregnancy. The occurrence of pre-eclampsia was 5% in white, 9% in Hispanic, and 11% in African American patients and this may reflect disproportionate risk of developing pre-eclampsia among ethnic groups. Additionally, black patients were also shown to have a disproportionately higher risk of dying from eclampsia.

Mechanism
The mechanisms of eclampsia and preeclampsia are not definitively understood, but following provides some insight. The presence of a placenta is required, and eclampsia resolves if it is removed. Reduced blood flow to the placenta (placental hypoperfusion) may be a key feature of the process. It is typically accompanied by increased sensitivity of the maternal vasculature to agents which cause constriction of the small arteries, leading to reduced blood flow to multiple organs. Vascular dysfunction-associated maternal conditions such as Lupus, hypertension, and renal disease, or obstetric conditions that increase placental volume without an increase in placental blood flow (such as multifetal gestation) may increase risk for pre-eclampsia. Also, activation of the coagulation cascade can lead to microthrombi formation, which may further impair blood flow. Thirdly, increased vascular permeability results in the shift of extracellular fluid from the blood to the interstitial space which reduces blood flow and causes edema. These events can lead to hypertension, renal dysfunction, pulmonary dysfunction, hepatic dysfunction, and cerebral edema with cerebral dysfunction and convulsions. In clinical context, increased platelet and endothelial activation may be detected before symptoms appear.

Hypoperfusion of the placenta is associated with abnormal modelling of the fetal–maternal placental interface that may be immunologically mediated. The pathogenesis of pre-eclampsia is poorly understood and may be attributed to factors related to the woman and placenta since pre-eclampsia is seen in molar pregnancies absent of a fetus or fetal tissue. The placenta normally produces the potent vasodilator adrenomedullin but it is reduced in pre-eclampsia and eclampsia. Other vasodilators, including prostacyclin, thromboxane A2, nitric oxide, and endothelins, are reduced in eclampsia and may lead to vasoconstriction.

Eclampsia is associated with hypertensive encephalopathy in which cerebral vascular resistance is reduced, leading to increased blood flow to the brain, cerebral edema and resultant convulsions. An eclamptic convulsion usually does not cause chronic brain damage unless intracranial haemorrhage occurs.

Diagnosis
If a pregnant woman has already been diagnosed with pre-eclampsia during the current pregnancy and then develops a seizure, she may be assigned a 'clinical diagnosis' of eclampsia without further workup. While seizures are most common in the third trimester, they may occur any time from 20 weeks of pregnancy until 6 weeks after birth. Because pre-eclampsia and eclampsia are common conditions in women, eclampsia can be assumed to be the correct diagnosis until proven otherwise in pregnant or postpartum women who experience seizures. However, if a woman has a seizure and it is unknown whether or not they have pre-eclampsia, testing can help make the diagnosis clear.

Pre-eclampsia is diagnosed when repeated blood pressure measurements are greater or equal to 140/90mmHg, in addition to any signs of organ dysfunction, including: proteinuria, thrombocytopenia, renal insufficiency, impaired liver function, pulmonary edema, cerebral symptoms, or abdominal pain.

Vital signs
One of the core features of pre-eclampsia is the new onset of high blood pressure. Blood pressure is a measurement of two numbers: systolic blood pressure and diastolic blood pressure. A systolic blood pressure (the top number) of greater than 140 mmHg and/or a diastolic blood pressure (the bottom number) of greater than 90 mmHg is higher than the normal range. If the blood pressure is high on at least two separate occasions after the first 20 weeks of pregnancy and the woman has signs of organ dysfunction (e.g. proteinuria), then they meet the criteria for a diagnosis of pre-eclampsia. If the systolic blood pressure is greater than 160 or the diastolic pressure is greater than 110, the hypertension is considered to be severe.

Laboratory testing
Another common feature of pre-eclampsia is proteinuria, which is the presence of excess protein in the urine. To determine if proteinuria is present, the urine can be collected and tested for protein; if there is 0.3 grams of protein or more in the urine of a pregnant woman collected over 24 hours, this is one of the diagnostic criteria for pre-eclampsia and raises the suspicion that a seizure is due to eclampsia.

In cases of severe eclampsia or pre-eclampsia, the woman can have low levels of platelets in the blood, a condition termed thrombocytopenia. A complete blood count, or CBC, is a test of the blood that can be performed to check platelet levels.

Other investigations include: kidney function test, liver function tests (LFT), coagulation screen, 24-hour urine creatinine, and fetal/placental ultrasound.

Differential diagnosis
Convulsions during pregnancy that are unrelated to pre-eclampsia need to be distinguished from eclampsia. Such disorders include seizure disorders as well as brain tumor, aneurysm of the brain, and medication- or drug-related seizures. Usually, the presence of the signs of severe pre-eclampsia precede and accompany eclampsia, facilitating the diagnosis.

Prevention
Detection and management of pre-eclampsia is critical to reduce the risk of eclampsia. The USPSTF recommends regular checking of blood pressure through pregnancy in order to detect preeclampsia. Appropriate management of a woman with pre-eclampsia generally involves the use of magnesium sulfate to prevent eclamptic seizures. In some cases, low-dose aspirin has been shown to decrease the risk of pre-eclampsia in women, especially when taken in the late first trimester.

Treatment
The four goals of the treatment of eclampsia are to stop and prevent further convulsions, to control the elevated blood pressure, to deliver the baby as promptly as possible, and to monitor closely for the onset of multi-organ failure.

Convulsions
Convulsions are prevented and treated using magnesium sulfate. The study demonstrating the effectiveness of magnesium sulfate for the management of eclampsia was first published in 1955. Effective anticonvulsant serum levels range from 2.5 to 7.5 mEq/L, however the ideal dosing regime (dose, route of administration, timing of dosing) to prevent and treat eclampsia is not clear.

With intravenous administration, the onset of anticonvulsant action is fast and lasts about 30 minutes. Following intramuscular administration the onset of action is about one hour and lasts for three to four hours. Magnesium is excreted solely by the kidneys at a rate proportional to the plasma concentration (concentration in the blood) and glomerular filtration (rate at which the blood is filtered through the kidneys). Magnesium sulfate is associated with several minor side effects; serious side effects are uncommon, occurring at elevated magnesium serum concentrations greater than 7.0 mEq/L. Serious toxicity can be counteracted with calcium gluconate.

Even with therapeutic serum magnesium concentrations, recurrent convulsions may occur, and additional magnesium may be needed, but with close monitoring for respiratory, cardiac, and neurological depression. If magnesium administration with resultant high serum concentrations fails to control convulsions, the addition of other intravenous anticonvulsants may be used and intubation and mechanical ventilation may be initiated. It is important to avoid magnesium toxicity, including thoracic muscle paralysis, which could cause respiratory failure and death.

Magnesium sulfate results in better outcomes than diazepam, phenytoin or a combination of chlorpromazine, promethazine, and pethidine.

Blood pressure management
Blood pressure is controlled to prevent stroke, which accounts for 15 to 20 percent of deaths in women with eclampsia. Common drugs used for blood pressure control during eclampsia are hydralazine or labetalol, due to their effectiveness, lack of negative effects on the fetus, and mechanism of action. Blood pressure management is indicated with a diastolic blood pressure above 105–110 mm Hg. Normal blood pressure levels for pregnant women vary between trimesters and as so blood pressure management will be tailored accordingly.

Delivery
If the baby has not yet been delivered, steps need to be taken to stabilize the woman and deliver her speedily. This needs to be done even if the baby is immature, as the eclamptic condition is unsafe for both baby and mother. As eclampsia is a manifestation of a type of non-infectious multiorgan dysfunction or failure, other organs (liver, kidney, lungs, cardiovascular system, and coagulation system) need to be assessed in preparation for a delivery (often a caesarean section), unless the woman is already in advanced labor. Regional anesthesia for caesarean section is contraindicated when a coagulopathy has developed.

There is limited to no evidence in favor of a particular delivery method for women with eclampsia. Therefore, the delivery method of choice is an individualized decision.

Monitoring
Invasive hemodynamic monitoring may be elected in an eclamptic woman at risk for or with heart disease, kidney disease, refractory hypertension, pulmonary edema, or poor urine output.

Etymology
The Greek noun ἐκλαμψία,, denotes a "light burst"; metaphorically, in this context, "sudden occurrence." The Neo-Latin term first appeared in Johannes Varandaeus’ 1620 treatise on gynaecology Tractatus de affectibus Renum et Vesicae. The term 'toxemia of pregnancy' is no longer recommended: placental toxins are not the cause of eclampsia occurrences, as previously believed.

Notable deaths from eclampsia

 * Tori Bowie (fetus died too)

Popular culture

 * In Downton Abbey, a historical drama television series, the character Lady Sybil dies (in series 3, episode 5) of eclampsia shortly after child birth.
 * In Call the Midwife, a medical drama television series set in London in the 1950s and 1960s, the character (in series 1, episode 4) named Margaret Jones is struck with pre-eclampsia, ultimately proceeding from a comatose condition to death. The term "toxemia" was also used for the condition, in the dialogue.
 * In House M.D., a medical drama television series set in the U.S., Dr. Cuddy, the hospital director, adopts a baby whose teenage mother dies from eclampsia and had no other parental figures available.
 * In The Lemon Drop Kid, the main character's wife dies of eclampsia shortly after giving birth to a boy.
 * In Fringe, a science fiction series, the character Olivia (in the parallel universe) is diagnosed with a fictionalized version of the disorder, called "viral-propagated eclampsia", which threatens her and her unborn child (series 3, episode 18).

title: Eclampsia