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Operator (physics)

In physics, an operator is a function over a space of physical states onto another space of physical states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group useful in this context). Because of this, they are useful tools in classical mechanics. Operators are even more important in quantum mechanics, where they form an intrinsic part of the formulation of the theory.

Operators in classical mechanics
In classical mechanics, the movement of a particle (or system of particles) is completely determined by the Lagrangian $$L(q, \dot{q}, t)$$ or equivalently the Hamiltonian $$H(q, p, t)$$, a function of the generalized coordinates q, generalized velocities $$\dot{q} = \mathrm{d} q / \mathrm{d} t$$ and its conjugate momenta:

 * $$p = \frac{\partial L}{\partial \dot{q}}$$

If either L or H is independent of a generalized coordinate q, meaning the L and H do not change when q is changed, which in turn means the dynamics of the particle are still the same even when q changes, the corresponding momenta conjugate to those coordinates will be conserved (this is part of Noether's theorem, and the invariance of motion with respect to the coordinate q is a symmetry). Operators in classical mechanics are related to these symmetries.

More technically, when H is invariant under the action of a certain group of transformations G:

 * $$S\in G, H(S(q,p))=H(q,p)$$.

The elements of G are physical operators, which map physical states among themselves.

Table of classical mechanics operators
where $$R(\hat{\boldsymbol{n}}, \theta)$$ is the rotation matrix about an axis defined by the unit vector $$\hat{\boldsymbol{n}}$$ and angle θ.

Generators
If the transformation is infinitesimal, the operator action should be of the form

 * $$ I + \epsilon A, $$

where $$I$$ is the identity operator, $$\epsilon$$ is a parameter with a small value, and $$A$$ will depend on the transformation at hand, and is called a generator of the group. Again, as a simple example, we will derive the generator of the space translations on 1D functions.

As it was stated, $$T_a f(x)=f(x-a)$$. If $$a=\epsilon$$ is infinitesimal, then we may write

 * $$T_\epsilon f(x)=f(x-\epsilon)\approx f(x) - \epsilon f'(x).$$

This formula may be rewritten as

 * $$T_\epsilon f(x) = (I-\epsilon D) f(x)$$

where $$D$$ is the generator of the translation group, which in this case happens to be the derivative operator. Thus, it is said that the generator of translations is the derivative.

The exponential map
The whole group may be recovered, under normal circumstances, from the generators, via the exponential map. In the case of the translations the idea works like this.

The translation for a finite value of $$a$$ may be obtained by repeated application of the infinitesimal translation:

 * $$T_a f(x) = \lim_{N\to\infty} T_{a/N} \cdots T_{a/N} f(x)$$

with the $$\cdots$$ standing for the application $$N$$ times. If $$N$$ is large, each of the factors may be considered to be infinitesimal:

 * $$T_a f(x) = \lim_{N\to\infty} \left(I - \frac{a}{N} D\right)^N f(x).$$

But this limit may be rewritten as an exponential:

 * $$T_a f(x) = \exp(-aD) f(x).$$

To be convinced of the validity of this formal expression, we may expand the exponential in a power series:

 * $$T_a f(x) = \left( I - aD + {a^2 D^2 \over 2!} - {a^3 D^3 \over 3!} + \cdots \right) f(x).$$

The right-hand side may be rewritten as

 * $$f(x) - af'(x) + \frac{a^2}{2!} f''(x) - \frac{a^3}{3!} f^{(3)}(x) + \cdots$$

which is just the Taylor expansion of $$f(x-a)$$, which was our original value for $$T_a f(x)$$.

The mathematical properties of physical operators are a topic of great importance in itself. For further information, see C*-algebra and Gelfand–Naimark theorem.

Operators in quantum mechanics
The mathematical formulation of quantum mechanics (QM) is built upon the concept of an operator.

Physical pure states in quantum mechanics are represented as unit-norm vectors (probabilities are normalized to one) in a special complex Hilbert space. Time evolution in this vector space is given by the application of the evolution operator.

Any observable, i.e., any quantity which can be measured in a physical experiment, should be associated with a self-adjoint linear operator. The operators must yield real eigenvalues, since they are values which may come up as the result of the experiment. Mathematically this means the operators must be Hermitian. The probability of each eigenvalue is related to the projection of the physical state on the subspace related to that eigenvalue. See below for mathematical details about Hermitian operators.

In the wave mechanics formulation of QM, the wavefunction varies with space and time, or equivalently momentum and time (see position and momentum space for details), so observables are differential operators.

In the matrix mechanics formulation, the norm of the physical state should stay fixed, so the evolution operator should be unitary, and the operators can be represented as matrices. Any other symmetry, mapping a physical state into another, should keep this restriction.

Wavefunction
The wavefunction must be square-integrable (see Lp spaces), meaning:

 * $$\iiint_{\R^3} |\psi(\mathbf{r})|^2 \, d^3\mathbf{r} = \iiint_{\R^3} \psi(\mathbf{r})^*\psi(\mathbf{r}) \, d^3\mathbf{r} < \infty $$

and normalizable, so that:

 * $$\iiint_{\R^3} |\psi(\mathbf{r})|^2 \, d^3\mathbf{r} = 1 $$

Two cases of eigenstates (and eigenvalues) are:
 * for discrete eigenstates $$ | \psi_i \rangle $$ forming a discrete basis, so any state is a sum $$|\psi\rangle = \sum_i c_i|\phi_i\rangle$$ where ci are complex numbers such that |ci|2 = ci*ci is the probability of measuring the state $$|\phi_i\rangle$$, and the corresponding set of eigenvalues ai is also discrete - either finite or countably infinite. In this case, the inner product of two eigenstates is given by $$\langle \phi_i \vert \phi_j\rangle=\delta_{ij}$$, where $$\delta_{mn}$$ denotes the Kronecker Delta. However,
 * for a continuum of eigenstates $$ | \psi_i \rangle $$ forming a continuous basis, any state is an integral $$|\psi\rangle = \int c(\phi) \, d\phi|\phi\rangle $$ where c(φ) is a complex function such that |c(φ)|2 = c(φ)*c(φ) is the probability of measuring the state $$|\phi\rangle$$, and there is an uncountably infinite set of eigenvalues a. In this case, the inner product of two eigenstates is defined as $$\langle \phi' \vert \phi\rangle=\delta(\phi - \phi')$$, where here $$\delta(x-y)$$ denotes the Dirac Delta.

Linear operators in wave mechanics
Let $ψ$ be the wavefunction for a quantum system, and $$\hat{A}$$ be any linear operator for some observable $A$ (such as position, momentum, energy, angular momentum etc.). If $ψ$ is an eigenfunction of the operator $$\hat{A}$$, then

 * $$\hat{A} \psi = a \psi ,$$

where $a$ is the eigenvalue of the operator, corresponding to the measured value of the observable, i.e. observable $A$ has a measured value $a$.

If $ψ$ is an eigenfunction of a given operator $$\hat{A}$$, then a definite quantity (the eigenvalue $a$) will be observed if a measurement of the observable $A$ is made on the state $ψ$. Conversely, if $ψ$ is not an eigenfunction of $$\hat{A}$$, then it has no eigenvalue for $$\hat{A}$$, and the observable does not have a single definite value in that case. Instead, measurements of the observable $A$ will yield each eigenvalue with a certain probability (related to the decomposition of $ψ$ relative to the orthonormal eigenbasis of $$\hat{A}$$).

In bra–ket notation the above can be written;

 * $$\begin{align}

\hat{A} \psi &= \hat{A} \psi ( \mathbf{r} ) = \hat{A} \left\langle \mathbf{r} \mid \psi \right\rangle = \left\langle \mathbf{r} \left\vert \hat {A} \right\vert \psi \right\rangle \\ a \psi &= a \psi ( \mathbf{r} ) = a \left\langle \mathbf{r} \mid \psi \right\rangle = \left\langle \mathbf{r} \mid a \mid \psi \right\rangle \\ \end{align} $$

that are equal if $$ \left| \psi \right\rangle $$ is an eigenvector, or eigenket of the observable $A$.

Due to linearity, vectors can be defined in any number of dimensions, as each component of the vector acts on the function separately. One mathematical example is the del operator, which is itself a vector (useful in momentum-related quantum operators, in the table below).

An operator in n-dimensional space can be written:

 * $$ \mathbf{\hat{A}} = \sum_{j=1}^n \mathbf{e}_j \hat{A}_j $$

where ej are basis vectors corresponding to each component operator Aj. Each component will yield a corresponding eigenvalue $$a_j$$. Acting this on the wave function $ψ$:

 * $$ \mathbf{\hat{A}} \psi = \left( \sum_{j=1}^n \mathbf{e}_j \hat{A}_j \right) \psi = \sum_{j=1}^n \left( \mathbf{e}_j \hat{A}_j \psi \right) = \sum_{j=1}^n \left( \mathbf{e}_j a_j \psi \right) $$

in which we have used $$ \hat{A}_j \psi = a_j \psi .$$

In bra–ket notation:

 * $$\begin{align}

\mathbf{\hat{A}} \psi = \mathbf{\hat{A}} \psi ( \mathbf{r} ) = \mathbf{\hat{A}} \left\langle \mathbf{r} \mid \psi \right\rangle &= \left\langle \mathbf{r} \left\vert \mathbf{\hat{A}} \right\vert \psi \right\rangle \\ \left ( \sum_{j=1}^n \mathbf{e}_j \hat{A}_j \right ) \psi = \left( \sum_{j=1}^n \mathbf{e}_j \hat{A}_j \right) \psi ( \mathbf{r} ) = \left( \sum_{j=1}^n \mathbf{e}_j \hat{A}_j \right) \left\langle \mathbf{r} \mid \psi \right\rangle &= \left\langle \mathbf{r} \left\vert \sum_{j=1}^n \mathbf{e}_j \hat{A}_j \right\vert \psi \right\rangle \end{align}$$

Commutation of operators on Ψ
If two observables A and B have linear operators $$ \hat{A} $$ and $$ \hat{B} $$, the commutator is defined by,

 * $$ \left[ \hat{A}, \hat{B} \right] = \hat{A} \hat{B} - \hat{B} \hat{A} $$

The commutator is itself a (composite) operator. Acting the commutator on ψ gives:

 * $$ \left[ \hat{A}, \hat{B} \right] \psi = \hat{A} \hat{B} \psi - \hat{B} \hat{A} \psi . $$

If ψ is an eigenfunction with eigenvalues a and b for observables A and B respectively, and if the operators commute:

 * $$ \left[ \hat{A}, \hat{B} \right] \psi = 0, $$

then the observables A and B can be measured simultaneously with infinite precision, i.e., uncertainties $$ \Delta A = 0 $$, $$ \Delta B = 0 $$ simultaneously. ψ is then said to be the simultaneous eigenfunction of A and B. To illustrate this:

 * $$ \begin{align}

\left[ \hat{A}, \hat{B} \right] \psi &= \hat{A} \hat{B} \psi - \hat{B} \hat{A} \psi \\ & = a(b \psi) - b(a \psi) \\ & = 0 . \\ \end{align} $$

It shows that measurement of A and B does not cause any shift of state, i.e., initial and final states are same (no disturbance due to measurement). Suppose we measure A to get value a. We then measure B to get the value b. We measure A again. We still get the same value a. Clearly the state (ψ) of the system is not destroyed and so we are able to measure A and B simultaneously with infinite precision.

If the operators do not commute:

 * $$ \left[ \hat{A}, \hat{B} \right] \psi \neq 0, $$

they cannot be prepared simultaneously to arbitrary precision, and there is an uncertainty relation between the observables

 * $$\Delta A \Delta B \geq \left|\frac{1}{2}\langle[A, B]\rangle\right|$$

even if ψ is an eigenfunction the above relation holds. Notable pairs are position-and-momentum and energy-and-time uncertainty relations, and the angular momenta (spin, orbital and total) about any two orthogonal axes (such as Lx and Ly, or sy and sz, etc.).

Expectation values of operators on Ψ
The expectation value (equivalently the average or mean value) is the average measurement of an observable, for particle in region R. The expectation value $$\left\langle \hat{A} \right\rangle $$ of the operator $$ \hat{A} $$ is calculated from:

 * $$\left\langle \hat{A} \right\rangle = \int_R \psi^{*}\left( \mathbf{r} \right) \hat{A} \psi \left( \mathbf{r} \right) \mathrm{d}^3\mathbf{r} = \left\langle \psi \left| \hat{A} \right| \psi \right\rangle .$$

This can be generalized to any function F of an operator:

 * $$ \left\langle F \left( \hat{A} \right) \right\rangle = \int_R \psi(\mathbf{r})^{*} \left[ F \left( \hat{A} \right) \psi(\mathbf{r}) \right] \mathrm{d}^3 \mathbf{r} = \left\langle \psi \left| F \left( \hat{A} \right) \right| \psi \right\rangle, $$

An example of F is the 2-fold action of A on ψ, i.e. squaring an operator or doing it twice:

 * $$\begin{align}

F\left(\hat{A}\right) &= \hat{A}^2 \\ \Rightarrow \left\langle \hat{A}^2 \right\rangle &= \int_R \psi^{*} \left( \mathbf{r} \right) \hat{A}^2 \psi \left( \mathbf{r} \right) \mathrm{d}^3\mathbf{r} = \left\langle \psi \left\vert \hat{A}^2 \right\vert \psi \right\rangle \\ \end{align}\,\!$$

Hermitian operators
The definition of a Hermitian operator is:

 * $$\hat{A} = \hat{A}^\dagger$$

Following from this, in bra–ket notation:

 * $$\left\langle \phi_i \left| \hat{A} \right| \phi_j \right\rangle = \left\langle \phi_j \left| \hat{A} \right| \phi_i \right\rangle^*.$$

Important properties of Hermitian operators include:
 * real eigenvalues,
 * eigenvectors with different eigenvalues are orthogonal,
 * eigenvectors can be chosen to be a complete orthonormal basis,

Operators in matrix mechanics
An operator can be written in matrix form to map one basis vector to another. Since the operators are linear, the matrix is a linear transformation (aka transition matrix) between bases. Each basis element $$\phi_j $$ can be connected to another, by the expression:

 * $$A_{ij} = \left\langle \phi_i \left| \hat{A} \right| \phi_j \right\rangle,$$

which is a matrix element:

 * $$\hat{A} = \begin{pmatrix}

A_{11} & A_{12} & \cdots & A_{1n} \\ A_{21} & A_{22} & \cdots & A_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ A_{n1} & A_{n2} & \cdots & A_{nn} \\ \end{pmatrix} $$

A further property of a Hermitian operator is that eigenfunctions corresponding to different eigenvalues are orthogonal. In matrix form, operators allow real eigenvalues to be found, corresponding to measurements. Orthogonality allows a suitable basis set of vectors to represent the state of the quantum system. The eigenvalues of the operator are also evaluated in the same way as for the square matrix, by solving the characteristic polynomial:

 * $$ \det\left( \hat{A} - a \hat{I} \right) = 0 ,$$

where I is the n × n identity matrix, as an operator it corresponds to the identity operator. For a discrete basis:

 * $$ \hat{I} = \sum_i |\phi_i\rangle\langle\phi_i|$$

while for a continuous basis:

 * $$ \hat{I} = \int |\phi\rangle\langle\phi| \mathrm{d}\phi$$

Inverse of an operator
A non-singular operator $$\hat{A}$$ has an inverse $$ \hat{A}^{-1} $$ defined by:

 * $$ \hat{A}\hat{A}^{-1} = \hat{A}^{-1}\hat{A} = \hat{I} $$

If an operator has no inverse, it is a singular operator. In a finite-dimensional space, an operator is non-singular if and only if its determinant is nonzero:

 * $$ \det\left(\hat{A}\right) \neq 0$$

and hence the determinant is zero for a singular operator.

Table of QM operators
The operators used in quantum mechanics are collected in the table below (see for example ). The bold-face vectors with circumflexes are not unit vectors, they are 3-vector operators; all three spatial components taken together.

 * {| class="wikitable"

! scope="col" | Operator (common name/s) ! scope="col" | Cartesian component ! scope="col" | General definition ! scope="col" | SI unit ! scope="col" | Dimension ! Position \hat{x} &= x, & \hat{y} &= y, & \hat{z} &= z \end{align}$$ !rowspan="2"| Momentum $$ \begin{align} \hat{p}_x & = -i \hbar \frac{\partial}{\partial x}, & \hat{p}_y & = -i \hbar \frac{\partial}{\partial y}, & \hat{p}_z & = -i \hbar \frac{\partial}{\partial z} \end{align}$$ $$ \mathbf{\hat{p}} = -i \hbar \nabla \,\!$$ $$ \begin{align} \hat{p}_x = -i \hbar \frac{\partial}{\partial x} - qA_x \\ \hat{p}_y = -i \hbar \frac{\partial}{\partial y} - qA_y \\ \hat{p}_z = -i \hbar \frac{\partial}{\partial z} - qA_z \end{align}$$ $$ \begin{align} \mathbf{\hat{p}} & = \mathbf{\hat{P}} - q\mathbf{A} \\ & = -i \hbar \nabla - q\mathbf{A} \\ \end{align}\,\!$$ !rowspan="3"| Kinetic energy $$ \begin{align} \hat{T}_x & = -\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2} \\[2pt] \hat{T}_y & = -\frac{\hbar^2}{2m}\frac{\partial^2}{\partial y^2} \\[2pt] \hat{T}_z & = -\frac{\hbar^2}{2m}\frac{\partial^2}{\partial z^2} \\ \end{align} $$ $$ \begin{align} \hat{T} & = \frac{1}{2m}\mathbf{\hat{p}}\cdot\mathbf{\hat{p}} \\ & = \frac{1}{2m}(-i \hbar \nabla)\cdot(-i \hbar \nabla) \\ & = \frac{-\hbar^2 }{2m}\nabla^2 \end{align}\,\!$$ $$ \begin{align} \hat{T}_x & = \frac{1}{2m}\left(-i \hbar \frac{\partial}{\partial x} - q A_x \right)^2 \\ \hat{T}_y & = \frac{1}{2m}\left(-i \hbar \frac{\partial}{\partial y} - q A_y \right)^2 \\ \hat{T}_z & = \frac{1}{2m}\left(-i \hbar \frac{\partial}{\partial z} - q A_z \right)^2 \end{align}\,\!$$ $$ \begin{align} \hat{T} & = \frac{1}{2m}\mathbf{\hat{p}}\cdot\mathbf{\hat{p}} \\ & = \frac{1}{2m}(-i \hbar \nabla - q\mathbf{A})\cdot(-i \hbar \nabla - q\mathbf{A}) \\ & = \frac{1}{2m}(-i \hbar \nabla - q\mathbf{A})^2 \end{align}\,\!$$ $$ \begin{align} \hat{T}_{xx} & = \frac{\hat{J}_x^2}{2I_{xx}} \\ \hat{T}_{yy} & = \frac{\hat{J}_y^2}{2I_{yy}} \\ \hat{T}_{zz} & = \frac{\hat{J}_z^2}{2I_{zz}} \\ \end{align}\,\!$$ $$ \hat{T} = \frac{\mathbf{\hat{J}}\cdot\mathbf{\hat{J}}}{2I} \,\!$$ ! Potential energy ! Total energy
 * - style="vertical-align:top;"
 * - style="vertical-align:top;"
 * $$\begin{align}
 * $$ \mathbf{\hat{r}} = \mathbf{r} \,\!$$
 * m
 * [L]
 * - style="vertical-align:top;"
 * General
 * General
 * J s m−1 = N s
 * [M] [L] [T]−1
 * - style="vertical-align:top;"
 * Electromagnetic field
 * Electromagnetic field (uses kinetic momentum; A, vector potential)
 * J s m−1 = N s
 * [M] [L] [T]−1
 * - style="vertical-align:top;"
 * Translation
 * J
 * [M] [L]2 [T]−2
 * - style="vertical-align:top;"
 * Electromagnetic field
 * Electromagnetic field (A, vector potential)
 * J
 * [M] [L]2 [T]−2
 * - style="vertical-align:top;"
 * Rotation (I, moment of inertia)
 * Rotation
 * J
 * [M] [L]2 [T]−2
 * - style="vertical-align:top;"
 * N/A
 * $$ \hat{V} = V\left( \mathbf{r}, t \right) = V \,\!$$
 * J
 * [M] [L]2 [T]−2
 * - style="vertical-align:top;"
 * N/A
 * Time-dependent potential:

$$ \hat{E} = i \hbar \frac{\partial}{\partial t} \,\!$$

Time-independent:

$$ \hat{E} = E \,\!$$ ! Hamiltonian \hat{H} & = \hat{T} + \hat{V} \\ & = \frac{1}{2m}\mathbf{\hat{p}}\cdot\mathbf{\hat{p}} + V \\ & = \frac{1}{2m}\hat{p}^2 + V \\ \end{align} \,\!$$ ! Angular momentum operator \hat{L}_x & = -i\hbar \left(y {\partial \over \partial z} - z {\partial \over \partial y}\right) \\ \hat{L}_y & = -i\hbar \left(z {\partial \over \partial x} - x {\partial \over \partial z}\right) \\ \hat{L}_z & = -i\hbar \left(x {\partial \over \partial y} - y {\partial \over \partial x}\right) \end{align}$$ ! Spin angular momentum \hat{S}_x &= {\hbar \over 2} \sigma_x & \hat{S}_y &= {\hbar \over 2} \sigma_y & \hat{S}_z &= {\hbar \over 2} \sigma_z \end{align}$$
 * J
 * [M] [L]2 [T]−2
 * - style="vertical-align:top;"
 * $$ \begin{align}
 * $$ \begin{align}
 * J
 * [M] [L]2 [T]−2
 * - style="vertical-align:top;"
 * $$\begin{align}
 * $$\mathbf{\hat{L}} = \mathbf{r} \times -i\hbar \nabla $$
 * J s = N s m
 * [M] [L]2 [T]−1
 * - style="vertical-align:top;"
 * $$\begin{align}

where

$$\begin{align} \sigma_x &= \begin{pmatrix} 0 & 1 \\   1 & 0  \end{pmatrix} \\ \sigma_y &= \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix} \\ \sigma_z &= \begin{pmatrix} 1 & 0 \\    0 & -1  \end{pmatrix} \end{align}$$

are the Pauli matrices for spin-1/2 particles.
 * $$\mathbf{\hat{S}} = {\hbar \over 2} \boldsymbol{\sigma} \,\!$$

where σ is the vector whose components are the Pauli matrices. ! Total angular momentum \hat{J}_x & = \hat{L}_x + \hat{S}_x \\ \hat{J}_y & = \hat{L}_y + \hat{S}_y \\ \hat{J}_z & = \hat{L}_z + \hat{S}_z \end{align}$$ \mathbf{\hat{J}} & = \mathbf{\hat{L}} + \mathbf{\hat{S}} \\ & = -i\hbar \mathbf{r}\times\nabla + \frac{\hbar}{2}\boldsymbol{\sigma} \end{align}$$ ! Transition dipole moment (electric) \hat{d}_x & = q\hat{x}, & \hat{d}_y & = q\hat{y}, & \hat{d}_z & = q\hat{z} \end{align}$$
 * J s = N s m
 * [M] [L]2 [T]−1
 * - style="vertical-align:top;"
 * $$\begin{align}
 * $$\begin{align}
 * J s = N s m
 * [M] [L]2 [T]−1
 * - style="vertical-align:top;"
 * $$\begin{align}
 * $$\mathbf{\hat{d}} = q \mathbf{\hat{r}} $$
 * C m
 * [I] [T] [L]
 * }

Examples of applying quantum operators
The procedure for extracting information from a wave function is as follows. Consider the momentum p of a particle as an example. The momentum operator in position basis in one dimension is:

 * $$\hat{p} = -i\hbar\frac{\partial }{\partial x}$$

Letting this act on ψ we obtain:

 * $$\hat{p} \psi = -i\hbar\frac{\partial }{\partial x} \psi ,$$

if ψ is an eigenfunction of $$\hat{p}$$, then the momentum eigenvalue p is the value of the particle's momentum, found by:

 * $$ -i\hbar\frac{\partial }{\partial x} \psi = p \psi.$$

For three dimensions the momentum operator uses the nabla operator to become:

 * $$\mathbf{\hat{p}} = -i\hbar\nabla .$$

In Cartesian coordinates (using the standard Cartesian basis vectors ex, ey, ez) this can be written;

 * $$\mathbf{e}_\mathrm{x}\hat{p}_x + \mathbf{e}_\mathrm{y}\hat{p}_y + \mathbf{e}_\mathrm{z}\hat{p}_z = -i\hbar\left ( \mathbf{e}_\mathrm{x} \frac{\partial }{\partial x} + \mathbf{e}_\mathrm{y} \frac{\partial }{\partial y} + \mathbf{e}_\mathrm{z} \frac{\partial }{\partial z} \right ),$$

that is:

 * $$ \hat{p}_x = -i\hbar \frac{\partial}{\partial x}, \quad \hat{p}_y = -i\hbar \frac{\partial}{\partial y}, \quad \hat{p}_z = -i\hbar \frac{\partial}{\partial z} \,\!$$

The process of finding eigenvalues is the same. Since this is a vector and operator equation, if ψ is an eigenfunction, then each component of the momentum operator will have an eigenvalue corresponding to that component of momentum. Acting $$ \mathbf{\hat{p}} $$ on ψ obtains:

 * $$ \begin{align}

\hat{p}_x \psi & = -i\hbar \frac{\partial}{\partial x} \psi = p_x \psi \\ \hat{p}_y \psi & = -i\hbar \frac{\partial}{\partial y} \psi = p_y \psi \\ \hat{p}_z \psi & = -i\hbar \frac{\partial}{\partial z} \psi = p_z \psi \\ \end{align} \,\!$$

title: Operator (physics)


text:
Year of the Four Emperors

The Year of the Four Emperors, AD 69, was the first civil war of the Roman Empire, during which four emperors ruled in succession: Galba, Otho, Vitellius, and Vespasian. It is considered an important interval, marking the transition from the Julio-Claudians, the first imperial dynasty, to the Flavian dynasty. The period witnessed several rebellions and claimants, with shifting allegiances and widespread turmoil in Rome and the provinces.

In 68, Vindex, legate of Gallia Lugdunensis, revolted against Nero and encouraged Galba, governor of Hispania, to claim the Empire. The latter was proclaimed emperor by his legion in early April. He was notably supported by Otho, legate of Lusitania. Soon after, the legate of a legion in Africa, Clodius Macer, also rebelled against Nero. Vindex was defeated by the Rhine legions at the Battle of Vesontio, but they too rebelled against Nero. Finally, on 9 June 68, Nero committed suicide after being declared a public enemy by the Senate, which made Galba the new emperor. However, Galba was unable to establish his authority over the Empire, as several of his supporters were disappointed by his lack of gratitude. He especially adopted Piso Licinianus as heir (Galba was childless and elderly), instead of Otho, who, it had widely been assumed, would be chosen. Angered by this disgrace, Otho murdered Galba on 15 January with the help of the Praetorian Guard, and became emperor instead. Unlike Galba he rapidly earned considerable popularity, notably by bestowing favours and emulating Nero's successful early years.

Otho still had to face another claimant, Vitellius, who had been acclaimed by the legions of the Rhine on 1 January 69. Vitellius won the First Battle of Bedriacum on 14 April, defeating the emperor. Otho committed suicide the next day, and Vitellius was appointed emperor by the Senate on 19 April. The new emperor had little support outside of his veterans from the German legions, though. When Vespasian, legate of Syria, made his bid known, he received the allegiance of the legions of the Danube as well as many former supporters of Galba and Otho. After his acclamation in Alexandria on 1 July, Vespasian sent his friend Mucianus with a part of his army to fight Vitellius, but the Danubian legions commanded by Antonius Primus had not waited for Mucianus and defeated Vitellius' legions at the Second Battle of Bedriacum on 24 October. Vitellius was subsequently killed by a mob on 20 December. Mucianus arrived several days after and swiftly secured Vespasian's position in Rome (Primus had acted independently from him).

The death of Vitellius did not end the civil war, as the Rhine legions still rejected the rule of Vespasian and the new Flavian dynasty. Some Batavi provincials led by Civilis had fought them since Vitellius' acclamation. In 70, the new regime finally won the legions' surrender after negotiations, mainly because they lacked an alternative to Vespasian. Later, the new regime distorted the events—especially through the writings of the historian Tacitus—in order to remove the embarrassment of having relied on the Batavi to fight Roman legions. The Batavi were therefore said to have revolted against Rome, and the events dubbed the Revolt of the Batavi.

Vindex's revolt and fall of Nero (March–June 68)
The end of Nero's reign (54–68) was marked by political trials and plots, such as the Pisonian conspiracy in 65, showing the disenchantment of the senatorial elite towards the Emperor. In the winter of 67–68, Gaius Julius Vindex, the legate of Gallia Lugdunensis, looked for support among other governors and administrators in order to start a revolt against Nero. Aware of his relatively humble origins, Vindex did not covet the Empire for himself, nor did he name a candidate, probably to maximise his chances of finding someone interested. Plutarch tells that the people reached by Vindex forwarded his letters to Nero, except one: his southern neighbour Servius Sulpicius Galba, the governor of Hispania Tarraconensis, the largest Spanish province. In mid-March 68, Vindex proceeded with his plan and raised an army composed of Gallic tribesmen, which nevertheless cut short his attempts to win over the officers of the seven legions posted on the Rhine, whose soldiers would not accept fighting alongside Gauls. As a result, Vindex turned towards Galba, the only man who had not denounced him to Nero.

In early April 68, Galba accepted Vindex's proposition, and was acclaimed emperor in Carthago Nova (now Cartagena, Spain). He rapidly received support from officials of Baetica and Lusitania, the other two Iberian provinces, who provided him the money to raise the VII Galbiana, a second legion, in addition to the VI Victrix based in Galba's province.

Meanwhile, Vindex had to besiege his own former capital, Lugdunum, as its citizens were particularly devoted to Nero, which led Lucius Verginius Rufus, the governor of Germania Superior, to march on Vindex. He besieged Vesontio, capital of the Sequani, a tribe that supported Vindex, who therefore had to leave the siege of Lugdunum to come to their aid. Before Vesontio, Verginius and Vindex had a talk, during which they agreed to unite their forces against Nero. However, Verginius' legions ignored the agreement and charged the unprepared troops of Vindex, of whom up to 20,000 died, while Vindex committed suicide. Soon after, the Rhine legions proclaimed Verginius emperor, but he refused to accept. The soldiers were motivated by their hatred of Galba, as they had not forgotten his term as governor of Germania Superior in 39–41, during which he harshly repressed the legions that had supported the rebellion of Lentulus Gaetilicus in 39.

In Rome, Nero was unable to organise resistance to Galba's claim and was even thinking about fleeing to Egypt. The decisive move came from Nymphidius Sabinus, deputy prefect of the Praetorian Guard, who convinced his men to abandon Nero, by promising that Galba would give each of them 30,000 sesterces (equivalent to 10 years of wages), while he expected to be rewarded by the new emperor. On 9 June 68, the Senate declared Nero enemy of the state and proclaimed Galba emperor, which prompted Nero's suicide.

Galba
Galba was still in Spain when he received the news he had become emperor. He took at least a month to secure the Spanish provinces before leaving. He appointed Cluvius Rufus as his replacement in his own province, but also murdered several of his opponents there, including Obultronius Sabinus, the probable governor of Baetica. Escorted by the VII Galbiana, he left for Rome along the coastline, stopping at Narbo Martius. In Gaul, Galba executed Betuus Cilo, who as governor of Aquitania had fought Vindex. He also relieved Verginius Rufus from his post in Germania Superior because his acclamation by the legions could make him a dangerous rival. Meanwhile, in Rome, Nymphidius Sabinus realised that Galba had no intention of rewarding him with the post of praetorian prefect he coveted. He then pretended to be an illegitimate son of Caligula and started to conspire against Galba to make himself emperor. However, he was murdered by the Praetorian Guards when he tried to read before them a speech announcing his bid for the Empire.

During the first half of October, Galba finally completed his journey to Rome, which was described by Tacitus as "a long and bloody march", because of the officials he had murdered on his way and also for the massacre he committed on the Milvian Bridge, just before the city. In order to fight Galba, Nero had created the legion I Adiutrix from sailors of the Roman navy; when Galba arrived at Rome, the new legionaries pressed Galba to confirm their status, but he ordered his troops to charge them, killing thousands. He then accepted their request, but after they submitted to a decimation, a practice not used since Tiberius, which severely lowered the troops' morale. Galba also refused to pay the Praetorians the money promised by Nymphidius for overthrowing Nero.

Galba continued the practice set by Nero of appointing ineffectual men to the most important posts in the provinces: for example, he sent the old and disabled Hordeonius Flaccus to Germania Superior and Aulus Vitellius to Germania Inferior; the latter being mostly known at the time as a penniless glutton. In Rome, Galba considered with contempt anybody who had served under Nero. He only trusted three men who had been with him in Spain: Titus Vinius, Cornelius Laco, and Icelus, who had amassed money as Nero's protegés had, which likewise triggered popular resentment against the new emperor. Galba even turned against his first supporters, among them Aulus Caecina Alienus, former quaestor of Baetica, who had sent the money in his possession when Galba rebelled. The emperor had given him command of IV Macedonica in Germania Superior, but recalled him for embezzlement soon after.

Moreover, at the beginning of the civil year of 69 on 1 January, the legions of Germania Inferior refused to swear allegiance and obedience to Galba. On the following day, the legions acclaimed their governor Vitellius as emperor. Hearing the news of the loss of the Rhine legions, Galba panicked. He adopted a young senator, Lucius Calpurnius Piso Licinianus, as his successor. By doing so he offended many, above all Marcus Salvius Otho, an influential and ambitious nobleman who desired the honor for himself. Otho bribed the Praetorian Guard, already very unhappy with the emperor. When Galba heard about the coup d'état, he went to the streets in an attempt to stabilize the situation. It proved a mistake, because he could not attract any supporters. Shortly afterward the Praetorian Guard killed him in the Forum, along with Lucius and impaled their heads on poles.

Otho
On the day of Galba's murder, the Senate recognized Otho as emperor. They saluted the new emperor with relief. Although ambitious and greedy, Otho did not have a record of tyranny or cruelty and was expected to be a fair emperor. However, Otho's initial efforts to restore peace and stability were soon checked by the revelation that Vitellius had declared himself Imperator in Germania and had dispatched half of his army to march on Italy.

Backing Vitellius were the finest legions of the Empire, composed of veterans of the Germanic Wars, such as I Germanica and XXI Rapax. These would prove to be the best arguments for his bid for power. Otho was not keen to begin another civil war and sent emissaries to propose a peace and convey his offer to marry Vitellius's daughter. It was too late to reason; Vitellius's generals were leading half of his army toward Italy. After a series of minor victories, Otho suffered defeat in the First Battle of Bedriacum. Rather than flee and attempt a counter-attack, Otho decided to put an end to the anarchy and committed suicide. He had been emperor for a little more than three months.

Vitellius
On the news of Otho's suicide, the Senate recognized Vitellius as emperor. With this recognition, Vitellius set out for Rome; however, he faced problems from the start of his reign. The city remained very skeptical when Vitellius chose the anniversary of the Battle of the Allia (in 390 BC), a day of bad auspices according to Roman superstition, to accede to the office of Pontifex Maximus.

Events seemed to prove the omens right. With the throne tightly secured, Vitellius engaged in a series of banquets (Suetonius refers to three a day: morning, afternoon, and night) and triumphal parades that drove the imperial treasury close to bankruptcy. Debts quickly accrued, and moneylenders started to demand repayment. Vitellius showed his violent nature by ordering the torture and execution of those who dared to make such demands. With financial affairs in a state of calamity, Vitellius took to killing citizens who had named him as their heir, often together with any co-heirs. Moreover, he sought to rid himself of every possible rival, inviting them to the palace with promises of power, only to order their hasty assassination.

Vespasian
Meanwhile, the legions stationed in the African province of Egypt and the Middle Eastern provinces of Iudaea (Judea) and Syria acclaimed Vespasian as emperor. Vespasian had received a special command in Judaea from Nero in AD 67, with the task of putting down the First Jewish–Roman War. He gained the support of the governor of Syria, Gaius Licinius Mucianus. A strong force drawn from the Judaean and Syrian legions marched on Rome under the command of Mucianus. Vespasian himself travelled to Alexandria, where he was acclaimed emperor on 1 July, thereby gaining control of the vital grain supplies from Egypt. His son Titus remained in Judaea to deal with the Jewish rebellion. Before the eastern legions could reach Rome, the Danubian legions of the provinces of Raetia and Moesia also acclaimed Vespasian as emperor in August, and, led by Marcus Antonius Primus, invaded Italy. In October, the forces led by Primus won a crushing victory over Vitellius's army at the Second Battle of Bedriacum.

Surrounded by enemies, Vitellius made a last attempt to win the city to his side, distributing bribes and promises of power where needed. He tried to levy by force several allied tribes, such as the Batavians, but they refused. The Danube army was now very near Rome. Realizing the immediate threat, Vitellius made a last attempt to gain time by sending emissaries, accompanied by Vestal Virgins, to negotiate a truce and start peace talks. The following day, messengers arrived with news that the enemy was at the gates of the city. Vitellius went into hiding and prepared to flee, but decided on one last visit to the palace, where Vespasian's men caught and killed him. In seizing the capital, they burned down the temple of Jupiter.

The Senate acknowledged Vespasian as emperor the following day, 21 December 69.

Vespasian faced no direct threat to his imperial power after the death of Vitellius. He became the founder of the stable Flavian dynasty, which succeeded the Julio-Claudians. He died of natural causes in 79. The Flavians, each in turn, ruled from AD 69 to AD 96.

68

 * April – Galba, governor of Hispania Tarraconensis, and Vindex, governor of Gallia Lugdunensis rebel against Nero
 * May – The Rhine legions defeat and kill Vindex in Gaul
 * June – Nero is declared a public enemy (hostis) by the Senate (8 June) and commits suicide (9 June); Galba is recognised emperor
 * November – Vitellius nominated governor of Germania Inferior

69

 * 1 January – The Rhine legions refuse to swear loyalty to Galba
 * 2 January – Vitellius acclaimed emperor by the Rhine
 * 15 January – Galba killed by the Praetorian Guard; in the same day, the Senate recognizes Otho as emperor
 * 14 April – Vitellius defeats Otho
 * 16 April – Otho commits suicide; Vitellius recognised emperor
 * 1 July – Vespasian, commander of the Roman army in Judaea, proclaimed emperor by the legions of Egypt under Tiberius Julius Alexander
 * August – The Danubian legions announce support to Vespasian (in Syria) and invade Italy in September on his behalf
 * October – The Danubian army defeats Vitellius and Vespasian occupies Egypt
 * 20 December – Vitellius killed by soldiers in the Imperial Palace
 * 21 December – Vespasian recognized emperor

Ancient sources

 * Plutarch, Life of Galba.
 * Plutarch, Life of Otho.
 * Suetonius, Life of Galba.
 * Suetonius, Life of Otho.
 * Suetonius, Life of Vitellius.
 * Suetonius, Life of Vespasian.

Modern sources

 * T. Wiedemann "From Nero to Vespasian" in Alan K. Bowman, Edward Champlin, Andrew Lintott (editors), The Cambridge Ancient History, vol. X, The Augustan Empire, 43 B.C. – A.D. 69, Cambridge University Press, 1996.
 * M. Gwyn Morgan, 69 AD: The Year of Four Emperors, Oxford University Press, 2006. ISBN 978-0195124682.
 * M. Gwyn Morgan, 69 AD: The Year of Four Emperors, Oxford University Press, 2006. ISBN 978-0195124682.
 * M. Gwyn Morgan, 69 AD: The Year of Four Emperors, Oxford University Press, 2006. ISBN 978-0195124682.

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

title: Year of the Four Emperors


text:
Talk:Claudius Civilis

The reason for redirect is onomastic: if Civilis was a Julius, like Tacitus says and i believe him, he could not ever be a Claudius. Julius was the name adopted by romanized german in the time of Augustus and Caesar. Claudius was the name they adopted in the reign of Tiberius and his descendants. Civilis belonged to this first wave. Muriel Gottrop 17:39, 8 Aug 2003 (UTC)

title: Talk:Claudius Civilis


text:
USS Shaw (DD-68)

USS Shaw (DD-68) was a Sampson-class destroyer in the United States Navy during World War I. She was later transferred to the United States Coast Guard as CG-22.

Construction and commissioning
Shaw was laid down on 7 February 1916 by the Mare Island Navy Yard, launched on 9 December 1916, sponsored by Mrs. Virginia Kemper Lynch Millard, and commissioned on 9 April 1917.

World War I
Shaw sailed from Mare Island on 25 May 1917 and arrived at New York on 10 June 1917 ready for distant service. She sailed a week later as one of the escort of Group 4 of the Expeditionary Force from the United States to France. On 26 June, she fueled at sea from a tanker, and the convoy arrived at Quiberon Bay, France, on 1 July. On the 4th, she sailed from St. Nazaire and arrived at Cobh, Ireland, the next day. On 10 July, she began patrol and convoy escort duty based on Cobh, convoying eastbound and westbound ships through the submarine danger zone around Great Britain and Ireland, for the most part without incident. On 1 July 1918, she received an SOS from the torpedoed American transport, USS Covington (ID-1409), and rushed to her aid. On arrival, she found that Covington's survivors had been removed and the ship had been taken under tow. But, the crippled transport sank later in the day. On 25 September, a ship in Shaw's convoy was attacked by a submarine but not damaged.

On 9 October 1918, while escorting RMS Aquitania, Shaw's rudder jammed just as she was completing the right leg of a zigzag, leaving her headed directly towards the transport. A moment later, Aquitania struck Shaw, cutting off 90 ft of the destroyer's bow, mangling her bridge and setting her on fire. Shaw's crew brought her damage under control, and a skeleton crew of 21 men took the wreck 40 miles into port under her own power. Twelve men died in the accident.

Shaw remained under repair at Portsmouth, England, until 29 May 1919 when she sailed for the United States. She arrived at New York on 17 June 1919 and moved to the Philadelphia Navy Yard on 2 October where she joined the reserve destroyer group and was decommissioned on 21 June 1922.

United States Coast Guard
Shaw was struck from the Navy list on 25 March 1926 and transferred to the Coast Guard the same day, to serve in the Rum Patrol. She was returned to the Navy by the Coast Guard and reinstated on the Navy list effective 30 June 1933.

Her name was canceled on 1 November 1933 for assignment to a new destroyer, and the ship was struck again on 5 July 1934 and sold on 22 August 1934 for scrapping to Michael Plynn, Inc., Brooklyn, New York.

title: USS Shaw (DD-68)


text:
USS Shaw (DD-373)

USS Shaw (DD-373) was a Mahan-class destroyer and the second ship of the United States Navy to be named for Captain John Shaw, a naval officer. Commissioned in 1936, Shaw was plagued by construction deficiencies and was not fully operational until 1938. After training in the Atlantic, she was transferred to the Pacific and was berthed in a dry dock in Pearl Harbor on 7 December 1941.

Shaw sustained major damage from several bomb hits by Japanese forces during the attack on Pearl Harbor. The spectacular explosion of her forward magazine provided one of the most iconic photographs of the attack. She was repaired within a few months of the attack, and served in the Pacific through the rest of World War II, earning 11 battle stars.

Shaw was decommissioned in October 1945 and sold for scrap in July 1946.

History
Shaw was laid down on 1 October 1934 at the Philadelphia Naval Shipyard, Philadelphia, Pennsylvania; launched on 28 October 1935, sponsored by Miss Dorthy L. Tinker; and commissioned on 18 September 1936.

Following commissioning, Shaw remained at Philadelphia until April 1937, when she crossed the Atlantic on her shakedown cruise. Returning to Philadelphia on 18 June, she commenced a year of yard work to correct deficiencies before completing acceptance trials in June 1938. Shaw conducted training exercises in the Atlantic for the remainder of the year. She then transited to the Pacific and underwent overhaul at Mare Island from 8 January to 4 April 1939.

Shaw remained on the West Coast until April 1940, participating in various exercises and providing services to carriers and submarines operating in the area. In April, she sailed for Hawaii, where she participated in Fleet Problem XXI, an eight-phased operation for the defense of the Hawaiian area. She remained in the Hawaiian area until November, when she returned to the West Coast for overhaul.

Back in the Hawaiian area by mid-February 1941, Shaw operated in those waters until November, when she entered the Navy Yard at Pearl Harbor for repairs, drydocking in YFD-2.

Attack on Pearl Harbor

On 7 December, Shaw was still in auxiliary floating drydock YFD-2, receiving adjustments to her depth charge mechanisms. During the Japanese attack, she took three hits – two bombs through the forward machine gun platform, and one through the port wing of the bridge. Fires spread through the ship. By 0925, all fire-fighting facilities were exhausted, and the order to abandon ship was given. Efforts to flood the dock were only partially successful, and shortly after 0930, her forward magazine exploded.

Temporary repairs were made at Pearl Harbor during December 1941 and January 1942. On 9 February, Shaw steamed towards San Francisco, where repairs were completed, including the installation of a new bow, at the end of June. Following training in the San Diego, California, area, Shaw returned to Pearl Harbor on 31 August 1942.

Further service in World War II
For the next two months, she escorted convoys between the West Coast and Hawaii. In mid-October, as a unit of a carrier force centered on the USS Enterprise (CV-6), Shaw departed from Pearl Harbor and steamed westwardly. Meeting with a carrier force centered on USS Hornet (CV-8), the two carrier groups united as Task Force 61, and then moved north of the Santa Cruz Islands to intercept enemy forces headed to attack Guadalcanal.

By mid-morning on the 26th, both carrier groups were under attack. As an accompanying ship, USS Porter (DD-356), stopped to pick up survivors from a downed torpedo plane, she was torpedoed. Shaw went to Porter ' s assistance. Half an hour later, she was ordered to take off Porter's crew and sink the disabled destroyer. Periscope sightings followed by depth charge attacks delayed execution of the mission. By noon, however, the transfer was completed. An hour later, Porter was gone, and Shaw left the scene to rejoin the task force.

Two days later, Shaw headed for the New Hebrides, where she commenced escorting ships moving men and supplies to Guadalcanal. She continued that duty through November and December and into January 1943. On 10 January, while entering Nouméa Harbor, New Caledonia, Shaw ran aground on Sournois Reef. She was freed on the 15th, but extensive damage to her hull, propellers, and sound gear necessitated temporary repairs at Nouméa – followed by lengthy repairs and rearmament at Pearl Harbor, which took through September.

On 6 October, Shaw headed west again, reaching Nouméa on the 18th and Milne Bay, New Guinea, on the 24th. Now a unit of the 7th Amphibious Force, Shaw escorted reinforcements to Lae and Finschhafen for the remainder of October and during November. Following an unsuccessful diversionary assault by Army troops against Umtingalu, New Britain, on 15 December, Shaw recovered survivors from two rubber boats and escorted HMAS Westralia (1939) and USS Carter Hall (LSD-3) back to Buna, Papua New Guinea.

On 25 December, Shaw escorted units engaged in the assault against Cape Gloucester, where she provided gunfire support and served as fighter director ship. On the 26th, Shaw sustained casualties and damage when attacked by two "Vals." Thirty-six men were injured, three of whom later died of their wounds. The Shaw returned to Cape Sudest, New Guinea, on the 27th; she transferred her wounded and dead to shore facilities there, and continued on to Milne Bay for temporary repairs. Permanent repairs were completed at Hunter's Point, California, on 1 May 1944.

Shaw returned to Pearl Harbor on the 10th, joined the 5th Fleet there, and steamed toward the Marshall Islands on the 15th. She got underway from the Marshalls on 11 June with TF-52 to engage in the assault on Saipan Island. Four days later, the attack began. For the next three and one-half weeks, the destroyer rotated between screening and "call fire" support duties of the Marines on shore. In mid-July, Shaw was back in the Marshall Islands. On the 18th, Shaw got underway to return to the Mariana Islands accompanying the Guam assault forces. During the action that followed, Shaw performed escort and patrol duties.

Shaw departed the Marianas on 23 September. Following a tender repair availability at Eniwetok, she rejoined the 7th Amphibious Force on 20 October and headed for Leyte Gulf on the 25th. Convoy escort duties between the Philippines and New Guinea involved Shaw until the invasion of Luzon took place at Lingayen Gulf on 9 January 1945. From the 9th to the 15th, she performed screening, "call fire" support for the soldiers ashore, night illumination with star shells, and shore bombardment missions. Following this operation, Shaw was involved in the recapture of Manila Bay, Luzon. After the Luzon operations, Shaw supported the assault and occupation of Palawan Island during the period from 28 February to 4 March.

In early April, Shaw operated in the Visayas, setting two Japanese barges on fire off Bohol on 2 April. Damaged soon thereafter on an uncharted pinnacle, she underwent temporary repairs. On the 25th, she steamed toward the United States West Coast. Shaw arrived at San Francisco on 19 May. Repairs and upgrades to her systems continued into August. The work was completed on the 20th. Shaw then departed for the East Coast of the United States. Upon her arrival at Philadelphia, the warship was routed to New York City for deactivation. Decommissioned on 2 October 1945, her name was stricken from the Navy List two days later. Her hull was scrapped in July 1946.

Shaw earned 11 battle stars during World War II.

title: USS Shaw (DD-373)


text:
High Society (magazine)

High Society is an American pornographic magazine. In addition to hardcore pictorials of nude models, it also has feature articles and occasional celebrity pictorials.

History
High Society was first published in May 1976. Carl Ruderman hired the adult industry's first female men's magazine editor, Gloria Leonard, in 1977.

Leonard, an adult film star, is credited with the use of "900" and "976 phone numbers" to advertise upcoming magazine issues. This evolved into the very first "phone sex" lines.

In November 1981 a spin-off magazine, High Society Live!, debuted. Another venture was a celebrity focused publication, Celebrity Skin magazine, in 1986. The 10th Anniversary Issue of High Society, published May, 1986 featured Gail Thackray (Gail Harris) with a 10-page spread, Centerfold and Front cover. Over its 25-year run Margot Kidder, Ann-Margret and Barbra Streisand unsuccessfully attempted to sue the magazine after it published nude photos of them.

High Society has a pay-per-view TV channel.

The magazine is published by the Magna Publishing Group, which was acquired by 1-800-PHONESEX on December 22, 2015.

title: High Society (magazine)


text:
Alfred Sisley

Alfred Sisley (30 October 1839 – 29 January 1899) was an Impressionist landscape painter who was born and spent most of his life in France, but retained British citizenship. He was the most consistent of the Impressionists in his dedication to painting landscape en plein air (i.e., outdoors). He deviated into figure painting only rarely and, unlike Renoir and Pissarro, he found that Impressionism fulfilled his artistic needs.

Among his important works are a series of paintings of the River Thames, mostly around Hampton Court, executed in 1874, and landscapes depicting places in or near Moret-sur-Loing. The notable paintings of the Seine and its bridges in the former suburbs of Paris are like many of his landscapes, characterised by tranquillity, in pale shades of green, pink, purple, dusty blue and cream. Over the years Sisley's power of expression and colour intensity increased.

Biography
Sisley was born in Paris to affluent British parents. His father, William Sisley, was in the silk business, and his mother, Felicia Sell, was a cultivated music connoisseur.

In 1857, at the age of 18, Alfred Sisley was sent to London to study for a career in business, but he abandoned it after four years and returned to Paris in 1861. From 1862, he studied at the Paris École des Beaux-Arts within the atelier of Swiss artist Marc-Charles-Gabriel Gleyre, where he became acquainted with Frédéric Bazille, Claude Monet, and Pierre-Auguste Renoir. Together they would paint landscapes en plein air rather than in the studio, in order to capture the transient effects of sunlight realistically. This approach, innovative at the time, resulted in paintings more colourful and more broadly painted than the public was accustomed to seeing. Consequently, Sisley and his friends initially had few opportunities to exhibit or sell their work. Their works were usually rejected by the jury of the most important art exhibition in France, the annual Salon. During the 1860s, though, Sisley was in a better financial position than some of his fellow artists, as he received an allowance from his father.

In 1866, Sisley began a relationship with Eugénie Lescouezec (1834–1898; usually known as Marie Lescouezec), a Breton living in Paris. The couple had two children: son Pierre (born 1867) and daughter Jeanne (1869). At the time, Sisley lived not far from Avenue de Clichy and the Café Guerbois, the gathering-place of many Parisian painters.

In 1868, his paintings were accepted at the Salon, but the exhibition did not bring him financial or critical success; nor did subsequent exhibitions.

In 1870, the Franco-Prussian War began; as a result, Sisley's father's business failed, and the painter's sole means of support became the sale of his works. For the remainder of his life he would live in poverty, as his paintings did not rise significantly in monetary value until after his death. Occasionally, however, Sisley would be backed by patrons, and this allowed him, among other things, to make a few brief trips to Britain.

The first of these occurred in 1874, after the first independent Impressionist exhibition. The result of a few months spent south-west of London was a series of nearly twenty paintings of the non-tidal Thames at East Molesey and below its Hampton Court Bridge where the south bank becomes Thames Ditton which was later described by art historian Kenneth Clark as "a perfect moment of Impressionism."

Until 1880, Sisley lived and worked in the country west of Paris; then he and his family moved to a small village near Moret-sur-Loing, close to the forest of Fontainebleau, where the painters of the Barbizon school had worked earlier in the century. Here, as art historian Anne Poulet has said, "the gentle landscapes with their constantly changing atmosphere were perfectly attuned to his talents. Unlike Monet, he never sought the drama of the rampaging ocean or the brilliantly colored scenery of the Côte d'Azur."

In 1881, Sisley made a second brief voyage to Great Britain.

In 1897, Sisley and his partner visited Britain again, and were finally married in Wales at Cardiff Register Office on 5 August. They stayed at Penarth, where Sisley painted at least six oils of the sea and the cliffs. In mid-August they moved to the Osborne Hotel at Langland Bay on the Gower Peninsula, where he produced at least eleven oil paintings in and around Langland Bay and Rotherslade (then called Lady's Cove). They returned to France in October. This was Sisley's last voyage to his ancestral homeland. The National Museum Cardiff possesses two of his oil paintings of Penarth and Langland.

The following year Sisley applied for French citizenship, but was refused. A second application was made and supported by a police report, but illness intervened, and Sisley remained a British national until his death.

He died on 29 January 1899 of throat cancer in Moret-sur-Loing at the age of 59, a few months after the death of his wife.

Work
Sisley's student works are lost. His first landscape paintings are sombre, coloured with dark browns, greens, and pale blues. They were often executed at Marly and Saint-Cloud. Little is known about Sisley's relationship with the paintings of J. M. W. Turner and John Constable, which he may have seen in London, but some have suggested that these artists may have influenced his development as an Impressionist painter, as may have Gustave Courbet and Jean-Baptiste-Camille Corot.

He was inspired by the style and subject matter of previous modern painters Camille Pissarro and Edouard Manet. Among the Impressionists, Sisley has been overshadowed by Monet, whose work his resembles in style and subject matter, although Sisley's effects are more subdued. Described by art historian Robert Rosenblum as having "almost a generic character, an impersonal textbook idea of a perfect Impressionist painting", his work strongly invokes atmosphere, and his skies are always impressive. He concentrated on landscape more consistently than any other Impressionist painter.

Among Sisley's best-known works are Street in Moret and Sand Heaps, both owned by the Art Institute of Chicago, and The Bridge at Moret-sur-Loing, shown at Musée d'Orsay, Paris. Allée des peupliers de Moret (The Lane of Poplars at Moret) has been stolen three times from the Musée des Beaux-Arts in Nice – once in 1978 when on loan in Marseilles (recovered a few days later in the city's sewers), again in 1998 (when the museum's curator was convicted of the theft and jailed for five years with two accomplices), and finally in August 2007 (on 4 June 2008 French police recovered it and three other stolen paintings from a van in Marseilles).

A large number of fake Sisleys have been discovered. Sisley produced some 900 oil paintings, some 100 pastels and many other drawings.

During the Nazi period (1933–1945) a number of Sisley works were taken from Jewish art collectors by Nazis or their agents as part of the massive looting of Jews that preceded the Holocaust. On 18 June 2004 Sisley's Soleil de printemps, le Loing (1892) was restored to the family of Louis Hirsch, in a ceremony in Paris.

In 2008 a dispute erupted between Alain Dreyfus, an art dealer in Switzerland, and the auction house Christie's over a Sisley painting First Day of Spring in Moret, that was claimed by the Lindon family in court in Paris. Dreyfus said that Christie's had not sufficiently examined the work's history, or provenance, before putting it up for sale.

Also in 2008, the Sisley Bateaux en Réparation à Saint Mammès (1885) was recognised as having been looted by the Nazis and the subject of a settlement with the heirs of Benno and Frances Bernstein who had owned it before Nazi occupation.

Numerous Sisleys such as Winter Landscape were known to have been seized by the Nazi looting organisation known as the E.R.R.  and still have not been found.

The German Lost Art Foundation has 24 listings for Sisley.

Selected works

 * Avenue of Chestnut Trees near La Celle-Saint-Cloud (1865)
 * View of Montmartre from Cité des Fleurs to Les Batignolles (1869)
 * The Bridge at Villeneuve-la-Garenne (1872)
 * Ferry to the Ile-de-la-Loge – Flood (1872)
 * La Grande-Rue, Argenteuil (c. 1872)
 * Square in Argenteuil (Rue de la Chaussee) (1872)
 * Footbridge at Argenteuil (1872)
 * Chemin de la Machine, Louveciennes (1873)
 * Louveciennes. Sentier de la Mi-côte (1873)
 * Hampton Court Bridge (painting) (1874)
 * Molesey Weir – Morning (1874)
 * Regatta at Molesey (1874)
 * Under Hampton Court Bridge (1874)
 * The Terrace at Saint-Germain, Spring (1875)
 * The Small Meadows in Spring, By (c. 1881)

title: Alfred Sisley


text:
Legio III Augusta

Legio III Augusta ("Third Augustan Legion") was a legion of the Imperial Roman army. Its origin may have been the Republican 3rd Legion which served the general Pompey during his civil war against Gaius Julius Caesar (49–45 BC). It supported the general Octavian (later emperor Augustus) in his civil war against Mark Antony (31–30 BC). It was officially refounded in 30 BC, when Octavian achieved sole mastery of the Roman empire. In that year, it was deployed in the Roman province of Africa, where it remained until at least the late 4th century AD.

History and troop movements
The Legio III Augusta was placed in Africa to ensure a steady grain supply to Rome. Under Augustus, the African Proconsul had command over it and several other legions. By the end of Tiberius's reign, it was the only legion in Africa. Under Caligula, command of the army was withdrawn from the proconsul and given to a Propraetorial legate who answered directly to the emperor. The Legio III Augusta first set up camp at Haidra before 14. The base at Haidra was not large enough to support an entire legion; this suggests that the legion was split up. Desert warfare required a small and highly mobile fighting force and it was not unheard of for the emperor to split a legion into several vexillations and place them at separate fortresses. For the most part, whole legions were not moved into Africa but rather, small vexillations were formed from the armies of Germany and Pannonia and sent to help when needed.

The Roman military presence in North Africa was not always accepted or welcomed. Most notably in opposition to the Roman institution was Tacfarinas, a former Roman soldier turned Musulamii guerrilla leader. Tacfarinas is an example of the multiple rebellions against the expansion of the Roman Empire through military establishment and geographical positioning as well as the adequate and tactful response by the Third Augustan Legion.

The Berber tribes attacked the Augustan Legion when they were particularly vulnerable. It is reported that the first attacks were in 14 AD when the Legion had just completed its first road building project. The timing suggests that the Third Augustan Legion had not yet established its roots or an approving reputation. This first revolt was swiftly put down.

However, just three years later Tacfarinas started his attacks against the Romans. The guerrilla warfare tactics combined with Tacfarinas' novel approach to attack from the rear, created additional difficulties for the Third Augustan Legion in their efforts to defeat Tacfarinas. The manner in which Tacfarinas led his rebellions was of particular concern to the Third Augustan Legion. At first, Tacfarinas did not appear to be a great threat; his initial band of fighters was composed mainly of robbers and rebels. However, Tacfarinas' band of robbers soon gained the expertise and precision of the Roman Army. Tacfarinas traveled through North Africa collecting Roman soldiers left behind by the Third Augustan Legion; Tacitus describes this process as a "cherry picking " of sorts, using soldiers who had already been trained by the Roman army and using their skills against their creator. Tacfarinas created a new coalition from the collected Roman soldiers and North African citizens looking to rebel against the expansion of the Roman Empire into the Musulamii people, under his sole command.

With the traditional tactics used by the Roman army, the enemy was expected to attack in formation, as the Roman legions did. With the rebellion of Tacfarinas, Roman commanders had to change their mode of attack. The general of the Third Augustan Legion split up the army into small units of men that took orders from a commanding officer. These units of men were constantly battle ready, mobile, and trained to fight in the desert, anticipating attacks from Tacfarinas and his rebels. With this change in traditional tactics, Tacfarinas was defeated in a matter of years.

Tacfarinas' army was ultimately defeated and Tacfarinas himself committed suicide, however his revolts and rebellious efforts should not go unnoticed. The Third Augustan Legion had to master the revolutionary techniques of Tacfarinas' band of robbers and ex-soldiers to succeed in conquering Tacfarinas. The guerrilla warfare strategies that Tacfarinas displays are one of the many ways the Third Augustan Legion had to alter its defense techniques in order to settle rebels throughout North Africa. The Musulamii gang under leadership and control of Tacfarinas was just one example of rebellions that the Legion had to settle, however no army of rebels proved as difficult, incessant, or resilient as the guerrilla army under Tacfarinas.

The Third Augustan Legion was responsible for multiple building projects and the enforced the presence of the Roman Empire against rebellions in North Africa for over three hundred years. However, they influenced the frontier in ways other than through expansion and urbanization. Militarily, they reformed the structure of the frontier through cultural changes and their mere presence throughout Africa.

However, the legion was self-sufficient in protecting the African provinces for the majority of the time. Most threats that required reinforcements arose in Mauretania, as this was where the Moors were the most dangerous. The Third Augustan had around 5000–6000 men with about 10,000–15,000 auxiliary men stationed close by. Almost half of these soldiers were stationed in Mauretania Tingitana; the rest were positioned based on the military needs of that time. The Emperor Vespasian reunited the legion in a single fortress at Theveste, most likely in 75. In 115 or 120, the Legio III Augusta established their camp at Lambaesis where it remained for two centuries apart from the period 238–253.

The legion was disbanded in 238 AD "because of its role in putting down an African-based revolt against the emperor Maximinus in favor of the provincial governor Gordianus." Capelianus was a legate in the legion and the officer who (mis)used his legion to attack Gordian. For this reason, Gordian III disbanded the legion.

In 252, Valerian reformed the legion to deal with the "five people groups", a dangerous coalition of Berber tribes. The legion prevailed in 260 but the threat remained, and fortifications of Lambaesis were expanded over the following years. In 289, the struggle began again and the emperor Maximianus took personal control of the legion. The war lasted until 297 at which point the legion was victorious.

In the early 4th century, Diocletian personally put down a rebellious governor and immediately afterward, transferred the Legio III Augusta from Lambaesis to another, unknown base within the region. Diocletian often worked with the legion during the period of military anarchy from 235 to 284. He was particularly prolific with his building projects, many of which were in Africa. Most of the projects were aimed at either replacing earlier works destroyed during the period of military anarchy or repairing public improvements, which had been allowed to fall into decay. The Legion was the main labor resource for these projects. The legion was still mentioned as late as the early 5th century but the actual date of its final disbandment is unknown.

Urbanization
The Third Augustan Legion was not only a source of protection for the Roman Empire, but also largely responsible for the urbanization of the North African provinces. The Legion was initially stationed in Ammaedara (modern-day Haïdra) where they built their first military camp. From there. the legionaries invested part of their time in the construction of roads, bringing with it the expansion of the empire.

These new connections led to the development of new towns and cities for civilians, camps for the military and even colonies for the veterans. All three were usually distinct from each other, but as time progressed, civilian towns, military camps and veterants colonies tended to merge.

The Legion did not always build up an entire town. Often, civilians assisted in part of the building projects. The most common construction projects soldiers were requested to work on were aqueducts, fortifications and amphitheaters. Typically they were more involved with "monumental projects" rather than "pure architecture." The legion was therefore no solely a military force but also a corps of engineers and surveyors, which required an advanced mix of skills.

Roads
The first instance of military roads built by the Legio III Augusta happened in 14 AD: It connected their base in Ammaedara, through Thelepte, all the way to the Oasis of Gafsa. Further expansion occurred under the rule of Tiberius with a road from the Oasis of Gafsa to the Oasis of Gabes. Between these two cities, the Legion stopped for rest and created five stations.

The Legion sometimes followed the previously existing paved road or hard-packed dirt tracks between Punic or Berber towns, but they mainly created new roads. Their construction followed a distinct system. Since these roads were commonly built for the use of military movement, they needed to be kept as straight (for speed of movement) and as safe as possible (Therefore where possible built on higher ground, avoiding valleys). Due to the higher location, some roads were even built with a system to drain water. Calculations estimate that the total length of roads in North Africa during Roman rule reached about 19,300 kilometres.

Other important roads for the Legio III Augusta included the one linking Tebessa to the port of Hippo Regius. Its construction was imperative for more efficient delivery of supplies to the Legion and town. Another was the road from Tébessa (Tebessa) to Carthage; both roads were built during Vespasian's reign.

Finally, a road built under Trajan ran south across the mountains of the Gulf of Syrte. The strategic importance of the road is indicated by the number of forts built along it.

Some Emperors really encouraged building of roads. One in particular was Hadrian. He was deeply involved with the work of the Legio III Augusta and sought to make sure they were involved in building projects. the advantages of building roads was not restricted to military matters but provided economic incentives positive for the empire: For example, the long roads built in Leptis Magna helped open up the interior lands. Farmers seized this opportunity to plant more olive groves and therefore more oil was able to be exported to Rome.

Once towns began to take in close proximity to military camps, marks of separation were needed. Typically, arches were used to mark on roads (or above them) the distinction between the civilian area and the entrance into the Roman military camp. The Via Septimiana—a road built under the reign of Septimius Severus in the town of Lambaesis - illustrates this with the presence of a Triple Arch, marking the boundary where the Third Augustan Legion was within its military zone.

Aqueducts
The members of the Third Augustan Legion did not solely consist of military men. The Emperors made an effort to recruit some men that were experts in surveying and the mathematics of construction. There is good evidence of this from emperors Augustus, Hadrian and Trajan, who all held engineers responsible for both construction and the military. There were not always many of these talented men in Northern Africa so it was important to train other men for the job. Thus over time the army became a place to learn the technical skills of engineering and surveying. These men would become involved in the construction of the big duties like canals or aqueducts.

The construction of aqueducts was not an easy job. It was very difficult to make sure all the pipes were level and that the pressure was correct at both ends. The surveyor was responsible for calculating all these measurements beforehand and then leaving the directions with the procurator. They would most likely be handed off to an officer known as the mensor, whose position was comparable to that of a contractor, and he was in charge of overseeing the production. His main purpose was to assist in the layout of Roman camps and towns, and he directed the use of measuring instruments. One of the most commonly used devices was a groma which helped with the measurement of right angles.

However, the mensor and the legionaries were not always experts so the accuracy of the groma only helped to a certain extent. When this happened, surveyors had to be recalled for recalculations. There is a well-preserved inscription depicting this situation in Africa. The surveyor, Nonius Datus, wrote about his encounters with the Third Augustan Legion and how he had carefully surveyed, taken the measures of all the mountains and mapped out the axis for which the tunnel would need to be excavated. This he gave to the procurator. He even gave the information to the contractor to be sure everything was done correctly. As Datus' skills were so widely needed, he had to leave the Legion for four years expecting the construction would go along smoothly without him. The construction did not go according to plan. The legionaries were unable to dig the tunnels at the right measurement causing them to be completely off the intended line. It was up to Datus to fix the situation.

The surveyors knew how to properly construct these aqueducts. If they stayed to monitor the actual construction, the operation ran successfully. This can be witnessed by the vast number of aqueducts that stood hundreds of years, some of them even thousands. For example, the water springs from Jebel Zaghouan still bring water all the way to Tunis. Historian E. Lennox Manton says, "A large new pipeline takes it through those same conduits in the hills which were originally excavated by the legion." Although the pipping system was changed, the original layout is still used.

The Third Augustan Legion's camp bases
Augustus officially stationed his Third Legion in 30 BC at Ammaedara which was located in the Aures Mountains. There they protected the North African provinces for 105 years. Not much remains today, at the exception of ruins of theaters and churches that are quite recognizable. A large military cemetery has been found, most of the tombs being from legionaries. During their time stationed at Ammaedara, the Legion discovered the town of Sbeitla. Many soldiers were recruited from this town. Then in 75 AD the Legion's camp was moved to Theveste (present day Tebessa). However, many of the veterans stayed behind and were able to settle in town, several becoming farmers.

The move to Theveste in 75 AD was not very far—just a bit west of Ammaedara. They relocated for purely strategic reasons. It was believed that if they moved they would be closer to the enemy—the local tribes who had been uprising often. The Legion was dedicated to its protection so they wanted to make sure they were in the best place possible to do so. They settled the area and built their own town. This town was physically constructed according to the principle of Hippodamus, the grid layout. The few remains in modern time include just a few pieces of architecture: the arch to Caracalla, a temple to Minerva and ruins of an amphitheater. On the arch "medallions of Septimius Severus and Julia Domna still survive on its faces" and the temple is "…one of the three or four best-preserved temples of the Roman world," says John Ferguson, archaeologist, who explored the area. It is uncertain whether or not the Legion participated in the construction of these buildings, but it is clear that they were once in the town of their home base.

The Legion was moved a third and final time to station at Lambaesis in 128 AD. Once again this move was for strategic reasons as it was located in the Aures Mountains. This placement was the optimal location for control over the tribes. Originally they built their camp to be about 220 square yards following the same grid plan as they did at Theveste. As historian E. Lennox Manton describes the construction, he says it was built "to a rectangular plan with military precision." By the middle of the 2nd century, the town grew perhaps to four times its original size.

Throughout their stay at Lambaesis, columns, pillars with rounded niches and statues were all built around the town. They even paved a courtyard that was surrounded by porticos with rooms on three sides. Some of these rooms were just for the military guards and the Commander-in-chief. The fourth side consisted of a basilica. Probably one of the most "impressive" and "the most dominant memorials of Roman military might" was the praetorium built in Lambaesis. This praetorium served as the house of the commander — most likely the procurator. They also had baths and an amphitheater outside the camp. After some time civilians began to settle close by, but their area was marked off by an arch.

Veteran towns
One veteran town from the Third Augustan Legion (and actually other legions in the Empire) was Thuburbo Majus. Here colonies were arranged granting veterans with, at the most, ¾ an acre of land. Although they were considered retired, these veterans were still involved in the protection of the provinces. Therefore, their colonies were spread out according to the Legion's strategic plan, and members actually guarded the areas. They sometimes built towers or ditches to be even more secure. Regardless of the militaristic constructions in the town, there were still beautiful public buildings such as a forum, mosaic floors, baths, churches and temples.

Another town founded by Nerva especially for veterans was Cuicul (now Djémila), "the beautiful" in the 1st century. The Legion also helped protect this town just as in Thuburbo Majus. The town is located on a hill and the lower part was the original foundation. It was later extended up the hill as more and more commercial activity occurred. Originally, at the end of the 1st century, there was a forum built. This later became known as the North Forum because another was built in the 3rd century. The second forum included a beautiful temple to Septimius Severus. The staircase in the temple was wonderful, "…the most impressive flight of steps ever to be built to such an edifice in North Africa." There was a paved road that connected the two forums and upon walking, temples, buildings, homes and even the old market area could be seen. The wealthier veterans were able to construct baths and mosaics around the town. This made the area even more beauteous.

Thamugadi, or modern Timgad, was a town founded for the sole purpose of resettling veterans. Original inhabitants were given a small plot of land inside the city to build on and a small plot of land outside the city to farm. The city grew rapidly, fueled by the security provided by the nearby army camp and the economic prosperity of the mid-2nd century. Over the following generations, crops were sold to Rome and the economic status of the cities inhabitants shifted; some became wealthy while others remained in comparative poverty. The wealthy were not only able to build better homes for themselves, but also contributed to the town of Timgad by donating money for public monuments. The presence of a library within the town signifies a high standard of learning and indicates a high level of prosperity within this veteran settlement. Life after the military was apparently not as harsh as life in the military. The town's paved streets can still be walked on today, and it is possible to see the numerous public buildings as well. A library, a large theater (seating between 4000–5000 people) and most notably an amazing forum are all still standing. Trajan's arch is also visible. This was built to replace the Lambaesis Gate—a monument built on the street that led to Lambeasis. The town itself was most likely a very clean place. There are many baths throughout, probably close to 12–14.

Composition of the legion
Originally, the Legion was composed mainly of Italian soldiers, but by the 3rd century AD the legion was almost entirely of Punic and Libyan origin. Italy and Gaul were hard-pressed to cope with the demand for troops during the 2nd century. As a result, the African Legions had to get manpower from eastern and local sources.

Daily life
When the Legion was not campaigning, it was engaged in vast public works projects across North Africa. There was very little serious fighting between the end of Tacfarinas' rebellion in AD 24 and the assassination of Severus Alexander in 235. It is believed that a soldier in the Third Augustan during this time spent his days securing food, fuel, fodder, and completing general duties of camp life. They rebuilt structures, built roads, and repaired equipment. It is likely that they went out on routine patrols of the countryside. The Legio III Augusta built the thirty-nine kilometers of the Lambaesis aqueduct in eight months, and the Legion or its temporary successor kept the roads in repair throughout the period of military anarchy. The Legion built and fortified Lambaesis and a military colony at Thamugadi, which was settled largely by veterans of the legion.

Marriage of soldiers
As was the case throughout the empire, soldiers of the Third Augustan Legion were forbidden to marry. A mobile army might have been in state of forced celibacy but this was not possible or practical for soldiers in fixed frontier posts. Inscriptions from Lambaesis often mention women companions of soldiers, which indicate that although they did not marry during active duty, they did form relationships with local women.

title: Legio III Augusta


text:
Pedroche

Pedroche is a municipality in the province of Córdoba, Andalusia, Spain. It is located at the centre of Los Pedroches comarca, the northernmost part of Córdoba and Andalusia.

Landmarks
The Convento de Nuestra Señora de la Concepción is a mudéjar building the year 500 b.c.
 * Convent

Its construction is Catholic Monarchs, the stones of the Castle advantage previously demolished. Its clear structure can be seen Mudejar. It has three naves and can be classified among the religious monuments of the thirteenth century and fourteenth centuries, whose construction began after completion of the Reconquista by Fernando III. The head of the temple was built in the fifteenth century and was decorated with paintings of this era that can still be seen behind the Baroque altar. An original coffered ceiling in good condition, covers the central nave was made in the fifteenth century, all multicolored and beautiful execution. Striking is the small coffered ceiling over the Baptistery.
 * El Salvador (church)

Pedroche Tower national monument since 1979, is located on the highest part of town, next to the parish and Our Lady of the Castle. It is one of the most beautiful and graceful in Spain.
 * Renaissance Tower

Using materials of the castle began construction of the tower, probably in 1520. From the second body, in 1544, the architect Hernán Ruiz the Younger took over management of the works, which he held until 1558. Architect known for transforming the minaret tower of the mosque in Cordoba and the Giralda bell tower. Juan de Ochoa finished the work by placing the barrel in 1588, apparently on the master designs. The toweris composed four bodies, reachinga height of 56 meters. The first homer, the second octagonal bell tower is the third or square and the latter is cylindrical.

It is located some kilometers of town and keep the Pedroche patron, the Piedrasantas Virgin. Built in the sixteenth century baroque stand it added in the eighteenth century. Inside are kept seven wooden benches with the names of the seven villages of Pedroches, whose representatives are gathered here to discuss issues common to the villas.
 * Ermita de la Virgen de Piedrasantas

title: Pedroche


text:
Talk:Mischa Barton

Irish
Would some please revert or review this change titled "Irish citizenship". Although the edit appears to have been made in WP:GOODFAITH it does not provide any sources. Irish ancestry and the entitlement to apply for Irish citizenship does not mean Barton has done so or that she considers herself Irish. She may prefer to consider herself American, or British, but whatever she does this article should not make any assumptions and such statements should be fully and properly sourced. -- 109.76.154.158 (talk) 23:54, 21 May 2019 (UTC)

 * The IP is very correct. I have searched and can't find any RS. I have tagged the only mention now, and removed all others until it can be verified within WP:BLP. Arnkellow (talk) 19:34, 7 October 2020 (UTC)
 * Also from what I can gather it's Newry in Northern Ireland, where her mother is from: who is able to have Irish citizenship. There is no available info on this. Arnkellow (talk) 20:16, 7 October 2020 (UTC)

She has a dual citizenship. That said, she can't be a citizen of Republic of Ireland, since she has confirmed her 2 British and US-American passports. Therefore She also holds Irish citizenship has got to be removed. 62.46.203.255 (talk) 21:34, 13 June 2021 (UTC)

Links
Please add ill link to Operator movie. Thanks. --5.43.79.250 (talk) 02:02, 9 September 2019 (UTC)

Mischa Barton's mother is Nuala Quinn-Barton
Can somebody add a link to the first paragraph of the Early Life section linking to her mother's, Nuala Quinn-Barton, article?

--86.182.17.178 (talk) 02:44, 19 December 2020 (UTC)

Got to appreciate the high quality images used in this article
Just wow! — Preceding unsigned comment added by 149.117.222.13 (talk) 13:40, 13 June 2023 (UTC)

Roles
A Ring of Endless Light (2002) Disney Channel Original Movie co starring Ryan Merriman and Jared Padalecki 2600:1002:B00B:B6CF:AC67:3FF5:F29A:36A8 (talk) 04:01, 19 January 2024 (UTC)

title: Talk:Mischa Barton