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User talk:Rgaytan

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User talk:Earthchild

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User talk:Carlos Von Plonker

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Majorana equation

In physics, the Majorana equation is a relativistic wave equation. It is named after the Italian physicist Ettore Majorana, who proposed it in 1937 as a means of describing fermions that are their own antiparticle. Particles corresponding to this equation are termed Majorana particles, although that term now has a more expansive meaning, referring to any (possibly non-relativistic) fermionic particle that is its own anti-particle (and is therefore electrically neutral).

There have been proposals that massive neutrinos are described by Majorana particles; there are various extensions to the Standard Model that enable this. The article on Majorana particles presents status for the experimental searches, including details about neutrinos. This article focuses primarily on the mathematical development of the theory, with attention to its discrete and continuous symmetries. The discrete symmetries are charge conjugation, parity transformation and time reversal; the continuous symmetry is Lorentz invariance.

Charge conjugation plays an outsize role, as it is the key symmetry that allows the Majorana particles to be described as electrically neutral. A particularly remarkable aspect is that electrical neutrality allows several global phases to be freely chosen, one each for the left and right chiral fields. This implies that, without explicit constraints on these phases, the Majorana fields are naturally CP violating. Another aspect of electric neutrality is that the left and right chiral fields can be given distinct masses. That is, electric charge is a Lorentz invariant, and also a constant of motion; whereas chirality is a Lorentz invariant, but is not a constant of motion for massive fields. Electrically neutral fields are thus less constrained than charged fields. Under charge conjugation, the two free global phases appear in the mass terms (as they are Lorentz invariant), and so the Majorana mass is described by a complex matrix, rather than a single number. In short, the discrete symmetries of the Majorana equation are considerably more complicated than those for the Dirac equation, where the electrical charge $$U(1)$$ symmetry constrains and removes these freedoms.

Definition
The Majorana equation can be written in several distinct forms:
 * As the Dirac equation written so that the Dirac operator is purely Hermitian, thus giving purely real solutions.
 * As an operator that relates a four-component spinor to its charge conjugate.
 * As a 2×2 differential equation acting on a complex two-component spinor, resembling the Weyl equation with a properly Lorentz covariant mass term.

These three forms are equivalent, and can be derived from one-another. Each offers slightly different insight into the nature of the equation. The first form emphasises that purely real solutions can be found. The second form clarifies the role of charge conjugation. The third form provides the most direct contact with the representation theory of the Lorentz group.

Purely real four-component form
The conventional starting point is to state that "the Dirac equation can be written in Hermitian form", when the gamma matrices are taken in the Majorana representation. The Dirac equation is then written as
 * $$\left(\, -i\,\frac{\partial}{\partial t} - i\,\hat\alpha\cdot\nabla + \beta\, m\,\right)\,\psi = 0$$

with $$\hat\alpha$$ being purely real 4×4 symmetric matrices, and $$\beta$$ being purely imaginary skew-symmetric; as required to ensure that the operator (that part inside the parentheses) is Hermitian. In this case, purely real 4‑spinor solutions to the equation can be found; these are the Majorana spinors.

Charge-conjugate four-component form
The Majorana equation is
 * $$i \, {\partial\!\!\!\big /} \psi - m\, \psi_c = 0~$$

with the derivative operator $${\partial\!\!\!\big /}$$ written in Feynman slash notation to include the gamma matrices as well as a summation over the spinor components. The spinor $\,\psi_c\,$ is the charge conjugate of $\,\psi\,.$  By construction, charge conjugates are necessarily given by
 * $$\psi_c = \eta_c\, C\, {\overline\psi}^\mathsf{T}~$$

where $$\,(\cdot)^\mathsf{T}\,$$ denotes the transpose, $$\,\eta_c\,$$ is an arbitrary phase factor $$\,|\eta_c| = 1\,,$$ conventionally taken as $$\, \eta_c = 1 \,,$$ and $$\,C\,$$ is a 4×4 matrix, the charge conjugation matrix. The matrix representation of $$\,C\,$$ depends on the choice of the representation of the gamma matrices. By convention, the conjugate spinor is written as
 * $$\overline\psi = \psi^\dagger\, \gamma^0~.$$

A number of algebraic identities follow from the charge conjugation matrix $$C.$$ One states that in any representation of the gamma matrices, including the Dirac, Weyl, and Majorana representations, that $$\,C\,\gamma_\mu = -\gamma_\mu^\mathsf{T}\,C\,$$ and so one may write
 * $$\psi_c = -\eta_c\, \gamma^0 \, C \,\psi^* ~$$

where $$\,\psi^*\,$$ is the complex conjugate of $$\,\psi\,.$$ The charge conjugation matrix $$\,C\,$$ also has the property that
 * $$C^{-1} = C^\dagger = C^\mathsf{T} = -C $$

in all representations (Dirac, chiral, Majorana). From this, and a fair bit of algebra, one may obtain the equivalent equation:
 * $$ i\,{\partial\!\!\!\big /} \psi_c - m\,\psi = 0$$

$$

A detailed discussion of the physical interpretation of matrix $$C$$ as charge conjugation can be found in the article on charge conjugation. In short, it is involved in mapping particles to their antiparticles, which includes, among other things, the reversal of the electric charge. Although $$\psi^c$$ is defined as "the charge conjugate" of $$\psi,$$ the charge conjugation operator has not one but two eigenvalues. This allows a second spinor, the ELKO spinor to be defined. This is discussed in greater detail below.

Complex two-component form
The Majorana operator, $$\,\mathrm{D}_\text{L}\,,$$ is defined as
 * $$\mathrm{D}_\text{L} \equiv i\, \overline{\sigma}^\mu\,\partial_\mu + \eta\, m\, \omega\, K$$

where
 * $$\overline{\sigma}^\mu = \begin{bmatrix} \sigma^0 & -\sigma^1 & -\sigma^2 & -\sigma^3 \end{bmatrix} = \begin{bmatrix} I_2 & -\sigma_\text{x} & -\sigma_\text{y} & -\sigma_\text{z} \end{bmatrix}$$

is a vector whose components are the 2×2 identity matrix $$\,I_2\,$$ for $$\,\mu = 0\,$$ and (minus) the Pauli matrices for $$\,\mu \in \{1,\, 2,\, 3\}\,.$$ The $$\,\eta\,$$ is an arbitrary phase factor, $$\,|\eta| = 1\, ,$$ typically taken to be one: $$\,\eta = 1\,.$$ The $$\,\omega\,$$ is a 2×2 matrix that can be interpreted as the symplectic form for the symplectic group $$\, \operatorname{Sp}(2, \mathbb{C})\, ,$$ which is a double covering of the Lorentz group. It is
 * $$\omega = i\, \sigma_2 = \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}~,$$

which happens to be isomorphic to the imaginary unit "$i$" (i.e. $$\omega^2 = - I \,$$ and $$\, a\, I + b\, \omega \cong a + b\, i \in \mathbb{C}\,$$ for $$\, a, b \in \mathbb{R}$$) with the matrix transpose being the analog of complex conjugation.

Finally, the $$\,K\,$$ is a short-hand reminder to take the complex conjugate. The Majorana equation for a left-handed complex-valued two-component spinor $$\,\psi_\text{L}\,$$ is then
 * $$\mathrm{D}_\text{L} \psi_\text{L} = 0$$

or, equivalently,
 * $$i\, \overline{\sigma}^\mu\, \partial_\mu \psi_\text{L}(x) + \eta\, m\, \omega\, \psi^*_\text{L}(x) = 0$$

with $$\,\psi^*_\text{L}(x)\,$$ the complex conjugate of $$\,\psi_\text{L}(x)\,.$$ The subscript $L$ is used throughout this section to denote a left-handed chiral spinor; under a parity transformation, this can be taken to a right-handed spinor, and so one also has a right-handed form of the equation. This applies to the four-component equation as well; further details are presented below.

Key ideas
Some of the properties of the Majorana equation, its solution and its Lagrangian formulation are summarized here.
 * The Majorana equation is similar to the Dirac equation, in the sense that it involves four-component spinors, gamma matrices, and mass terms, but includes the charge conjugate $\psi_c$ of a spinor $\psi$ . In contrast, the Weyl equation is for two-component spinor without mass.
 * Solutions to the Majorana equation can be interpreted as electrically neutral particles that are their own anti-particle. By convention, the charge conjugation operator takes particles to their anti-particles, and so the Majorana spinor is conventionally defined as the solution where $$\psi=\psi_c.$$ That is, the Majorana spinor is "its own antiparticle". Insofar as charge conjugation takes an electrically charge particle to its anti-particle with opposite charge, one must conclude that the Majorana spinor is electrically neutral.
 * The Majorana equation is Lorentz covariant, and a variety of Lorentz scalars can be constructed from its spinors. This allows several distinct Lagrangians to be constructed for Majorana fields.
 * When the Lagrangian is expressed in terms of two-component left and right chiral spinors, it may contain three distinct mass terms: left and right Majorana mass terms, and a Dirac mass term. These manifest physically as two distinct masses; this is the key idea of the seesaw mechanism for describing low-mass neutrinos with a left-handed coupling to the Standard model, with the right-handed component corresponding to a sterile neutrino at GUT-scale masses.
 * The discrete symmetries of C, P and T conjugation are intimately controlled by a freely chosen phase factor on the charge conjugation operator. This manifests itself as distinct complex phases on the mass terms. This allows both CP-symmetric and CP-violating Lagrangians to be written.
 * The Majorana fields are CPT invariant, but the invariance is, in a sense "freer" than it is for charged particles. This is because charge is necessarily a Lorentz-invariant property, and is thus constrained for charged fields. The neutral Majorana fields are not constrained in this way, and can mix.

Two-component Majorana equation
The Majorana equation can be written both in terms of a real four-component spinor, and as a complex two-component spinor. Both can be constructed from the Weyl equation, with the addition of a properly Lorentz-covariant mass term. This section provides an explicit construction and articulation.

Weyl equation
The Weyl equation describes the time evolution of a massless complex-valued two-component spinor. It is conventionally written as

 * $$ \sigma^\mu\partial_\mu \psi = 0$$

Written out explicitly, it is

 * $$ I_2 \frac{\partial \psi}{\partial t} + \sigma_x\frac{\partial \psi}{\partial x} + \sigma_y\frac{\partial \psi}{\partial y} + \sigma_z\frac{\partial \psi}{\partial z} = 0$$

The Pauli four-vector is

 * $$ \sigma^\mu = \begin{pmatrix} \sigma^0 & \sigma^1 & \sigma^2 & \sigma^3 \end{pmatrix} = \begin{pmatrix} I_2 & \sigma_x & \sigma_y & \sigma_z \end{pmatrix}$$

that is, a vector whose components are the 2 × 2 identity matrix $$ I_2$$ for μ = 0 and the Pauli matrices for μ = 1, 2, 3. Under the parity transformation $$\vec x\to {\vec x}^\prime = -\vec x$$ one obtains a dual equation

 * $$ \bar{\sigma}^\mu\partial_\mu \psi = 0$$

where $$ \bar{\sigma}^\mu = \begin{pmatrix} I_2 & -\sigma_x & -\sigma_y & -\sigma_z \end{pmatrix}$$. These are two distinct forms of the Weyl equation; their solutions are distinct as well. It can be shown that the solutions have left-handed and right-handed helicity, and thus chirality. It is conventional to label these two distinct forms explicitly, thus:

\sigma^\mu\partial_\mu \psi_{\rm R} = 0 \qquad \bar{\sigma}^\mu\partial_\mu \psi_{\rm L} = 0~. $$

Lorentz invariance
The Weyl equation describes a massless particle; the Majorana equation adds a mass term. The mass must be introduced in a Lorentz invariant fashion. This is achieved by observing that the special linear group $$\operatorname{SL}(2,\mathbb{C})$$ is isomorphic to the symplectic group $$\operatorname{Sp}(2, \mathbb{C}).$$ Both of these groups are double covers of the Lorentz group $$\operatorname{SO}(1,3).$$ The Lorentz invariance of the derivative term (from the Weyl equation) is conventionally worded in terms of the action of the group $$\operatorname{SL}(2, \mathbb{C})$$ on spinors, whereas the Lorentz invariance of the mass term requires invocation of the defining relation for the symplectic group.

The double-covering of the Lorentz group is given by

 * $$\overline{\sigma}_\mu {\Lambda^\mu}_\nu = S \overline{\sigma}_\nu S^\dagger$$

where $$\Lambda \in \operatorname{SO}(1,3)$$ and $$S \in \operatorname{SL}(2, \mathbb{C})$$ and $$S^\dagger$$ is the Hermitian transpose. This is used to relate the transformation properties of the differentials under a Lorentz transformation $$x \mapsto x^\prime = \Lambda x$$ to the transformation properties of the spinors.

The symplectic group $$\operatorname{Sp}(2, \mathbb{C})$$ is defined as the set of all complex 2×2 matrices $$S$$ that satisfy

 * $$\omega^{-1} S^\textsf{T} \omega = S^{-1}$$

where
 * $$\omega = i\sigma_2 = \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}$$

is a skew-symmetric matrix. It is used to define a symplectic bilinear form on $$\mathbb{C}^2.$$ Writing a pair of arbitrary two-vectors $$u, v \in \mathbb{C}^2$$ as

u = \begin{pmatrix} u_1 \\ u_2 \end{pmatrix} \qquad v = \begin{pmatrix} v_1 \\ v_2 \end{pmatrix} $$

the symplectic product is
 * $$\langle u, v\rangle = -\langle v, u\rangle = u_1 v_2 - u_2 v_1 = u^\textsf{T} \omega v$$

where $$u^\textsf{T}$$ is the transpose of $$u~.$$ This form is invariant under Lorentz transformations, in that
 * $$\langle u, v\rangle = \langle Su, Sv\rangle$$

The skew matrix takes the Pauli matrices to minus their transpose:
 * $$\omega \sigma_k \omega^{-1} = -\sigma_k^\textsf{T}$$

for $$k = 1, 2, 3.$$ The skew matrix can be interpreted as the product of a parity transformation and a transposition acting on two-spinors. However, as will be emphasized in a later section, it can also be interpreted as one of the components of the charge conjugation operator, the other component being complex conjugation. Applying it to the Lorentz transformation yields

 * $$\sigma_\mu {\Lambda^\mu}_\nu = \left(S^{-1}\right)^\dagger \sigma_\nu S^{-1}$$

These two variants describe the covariance properties of the differentials acting on the left and right spinors, respectively.

Differentials
Under the Lorentz transformation $$x \mapsto x^\prime = \Lambda x$$ the differential term transforms as
 * $$\sigma^\mu\frac{\partial}{\partial x^\mu} \psi_{\rm R}(x)

\mapsto \sigma^\mu\frac{\partial}{\partial x^{\prime\mu}} \psi_{\rm R}(x^\prime) = \left(S^{-1}\right)^\dagger \sigma^\mu\frac{\partial}{\partial x^\mu} \psi_{\rm R}(x) $$

provided that the right-handed field transforms as
 * $$\psi_{\rm R}(x) \mapsto \psi^\prime_{\rm R}(x^\prime)= S\psi_{\rm R}(x)$$

Similarly, the left-handed differential transforms as
 * $$\overline{\sigma}^\mu\frac{\partial}{\partial x^\mu} \psi_{\rm L}(x)

\mapsto \overline{\sigma}^\mu\frac{\partial}{\partial x^{\prime\mu}} \psi_{\rm L}(x^\prime) = S \overline{\sigma}^\mu\frac{\partial}{\partial x^\mu} \psi_{\rm L}(x) $$ provided that the left-handed spinor transforms as
 * $$\psi_{\rm L}(x) \mapsto \psi^\prime_{\rm L}(x^\prime)= \left(S^\dagger\right)^{-1}\psi_{\rm L}(x)$$

$$

Mass term
The complex conjugate of the right handed spinor field transforms as

 * $$\psi^*_{\rm R}(x) \mapsto \psi^{\prime *}_{\rm R}(x^\prime) = S^*\psi^*_{\rm R}(x)$$

The defining relationship for $$\operatorname{Sp}(2, \mathbb{C})$$ can be rewritten as $$\omega S^* = \left(S^\dagger\right)^{-1} \omega\,.$$ From this, one concludes that the skew-complex field transforms as

 * $$m\omega\psi^*_{\rm R}(x) \mapsto m\omega\psi^{\prime *}_{\rm R}(x^\prime) = \left(S^\dagger\right)^{-1} m\omega\psi^*_{\rm R}(x)$$

This is fully compatible with the covariance property of the differential. Taking $$\eta = e^{i\phi}$$ to be an arbitrary complex phase factor, the linear combination

 * $$i\sigma^\mu \partial_\mu \psi_{\rm R}(x) + \eta m\omega\psi^*_{\rm R}(x)$$

transforms in a covariant fashion. Setting this to zero gives the complex two-component Majorana equation for the right-handed field. Similarly, the left-chiral Majorana equation (including an arbitrary phase factor $$\zeta$$) is

 * $$i\overline{\sigma}^\mu \partial_\mu \psi_{\rm L}(x) + \zeta m\omega\psi^*_{\rm L}(x) = 0$$

The left and right chiral versions are related by a parity transformation. As shown below, these square to the Klein–Gordon operator only if $$\eta = \zeta.$$ The skew complex conjugate $$\omega\psi^* = i\sigma^2\psi$$ can be recognized as the charge conjugate form of $$\psi~ ;$$ this is articulated in greater detail below. Thus, the Majorana equation can be read as an equation that connects a spinor to its charge-conjugate form.

Left and right Majorana operators
Define a pair of operators, the Majorana operators,
 * $$\begin{align}

\mathrm{D}_{\rm L} &= i\overline{\sigma}^\mu \partial_\mu + \zeta m\omega K & \mathrm{D}_{\rm R} &= i\sigma^\mu \partial_\mu + \eta m\omega K \end{align}$$ where $$K$$ is a short-hand reminder to take the complex conjugate. Under Lorentz transformations, these transform as
 * $$\begin{align}

\mathrm{D}_{\rm L} \mapsto \mathrm{D}^\prime_{\rm L} &= S \mathrm{D}_{\rm L} S^\dagger & \mathrm{D}_{\rm R} \mapsto \mathrm{D}^\prime_{\rm R} &= \left(S^\dagger\right)^{-1} \mathrm{D}_{\rm R} S^{-1} \end{align}$$ whereas the Weyl spinors transform as
 * $$\begin{align}

\psi_{\rm L} \mapsto \psi^\prime_{\rm L} &= \left(S^\dagger\right)^{-1} \psi_{\rm L} & \psi_{\rm R} \mapsto \psi^\prime_{\rm R} &= S \psi_{\rm R} \end{align}$$ just as above. Thus, the matched combinations of these are Lorentz covariant, and one may take
 * $$\begin{align}

\mathrm{D}_{\rm L} \psi_{\rm L} &= 0 & \mathrm{D}_{\rm R} \psi_{\rm R} &= 0 \end{align}$$ as a pair of complex 2-spinor Majorana equations.

The products $$\mathrm{D}_{\rm L} \mathrm{D}_{\rm R}$$ and $$\mathrm{D}_{\rm R} \mathrm{D}_{\rm L}$$ are both Lorentz covariant. The product is explicitly

\mathrm{D}_{\rm R} \mathrm{D}_{\rm L}  = \left(i\sigma^\mu \partial_\mu + \eta m\omega K\right) \left(i\overline{\sigma}^\mu \partial_\mu + \zeta m\omega K\right) = - \left(\partial_t^2 - \vec\nabla \cdot \vec\nabla + \eta\zeta^* m^2\right) = - \left(\square + \eta\zeta^* m^2\right) $$ Verifying this requires keeping in mind that $$\omega^2 = -1$$ and that $$Ki = -iK~.$$ The RHS reduces to the Klein–Gordon operator provided that $$\eta\zeta^* = 1$$, that is, $$\eta = \zeta~.$$ These two Majorana operators are thus "square roots" of the Klein–Gordon operator.

Four-component Majorana equation
The real four-component version of the Majorana equation can be constructed from the complex two-component equation as follows. Given the complex field $$\psi_{\rm L}$$ satisfying $$\mathrm{D}_{\rm L} \psi_{\rm L} = 0$$ as above, define

 * $$\chi_{\rm R} \equiv -\eta \omega \psi^*_{\rm L}$$

Using the algebraic machinery given above, it is not hard to show that
 * $$\left(i \sigma^\mu \partial_\mu - \eta m\omega K\right)\chi_{\rm R} = 0$$

Defining a conjugate operator
 * $$\delta_{\rm R} = i \sigma^\mu \partial_\mu - \eta m\omega K$$

The four-component Majorana equation is then
 * $$\left(\mathrm{D}_{\rm L} \oplus \delta_{\rm R} \right)\left(\psi_{\rm L} \oplus \chi_{\rm R}\right) = 0$$

Writing this out in detail, one has
 * $$\mathrm{D}_{\rm L} \oplus \delta_{\rm R} =

\begin{bmatrix} \mathrm{D}_{\rm L} & 0 \\ 0 & \delta_{\rm R} \end{bmatrix} = i \begin{bmatrix} I & 0 \\ 0 & I \end{bmatrix} \partial_t + i \begin{bmatrix} -\sigma^k & 0 \\ 0 & \sigma^k \end{bmatrix} \nabla_k + m \begin{bmatrix} \eta \omega K & 0 \\ 0 & -\eta \omega K \end{bmatrix} $$

Multiplying on the left by
 * $$\beta = \gamma^0 =\begin{bmatrix} 0 & I \\ I & 0 \end{bmatrix} $$

brings the above into a matrix form wherein the gamma matrices in the chiral representation can be recognized. This is

\beta \left(\mathrm{D}_{\rm L} \oplus \delta_{\rm R}\right) = \begin{bmatrix} 0 & \delta_{\rm R} \\ \mathrm{D}_{\rm L} & 0 \end{bmatrix} = i \beta \partial_t + i \begin{bmatrix} 0 & \sigma^k \\ - \sigma^k & 0 \end{bmatrix} \nabla_k - m \begin{bmatrix} 0 & \eta \omega K \\ -\eta \omega K & 0 \end{bmatrix} $$

That is,

\beta \left(\mathrm{D}_{\rm L} \oplus \delta_{\rm R}\right) = i\gamma^\mu \partial_\mu - m \begin{bmatrix} 0 & \eta \omega K \\ -\eta \omega K & 0 \end{bmatrix} $$

Applying this to the 4-spinor
 * $$\psi_{\rm L} \oplus \chi_{\rm R}

= \begin{pmatrix} \psi_{\rm L} \\ \chi_{\rm R} \end{pmatrix} = \begin{pmatrix} \psi_{\rm L} \\ -\eta\omega\psi^*_{\rm L} \end{pmatrix} $$ and recalling that $$\omega^2 = -1$$ one finds that the spinor is an eigenstate of the mass term,

\begin{bmatrix} 0 & \eta \omega K \\ -\eta \omega K & 0 \end{bmatrix} \begin{pmatrix} \psi_{\rm L} \\ -\eta\omega\psi^*_{\rm L} \end{pmatrix} = \begin{pmatrix} \psi_{\rm L} \\ -\eta\omega\psi^*_{\rm L} \end{pmatrix} $$ and so, for this particular spinor, the four-component Majorana equation reduces to the Dirac equation
 * $$\left(i\gamma^\mu \partial_\mu - m\right) \begin{pmatrix}

\psi_{\rm L} \\ -\eta\omega\psi^*_{\rm L} \end{pmatrix} = 0 $$

The skew matrix can be identified with the charge conjugation operator (in the Weyl basis). Explicitly, this is
 * $$\mathsf{C} = \begin{bmatrix} 0 & \eta \omega K \\ -\eta \omega K & 0 \end{bmatrix} $$

Given an arbitrary four-component spinor $$\psi ~,$$ its charge conjugate is
 * $$\mathsf{C} \psi = \psi^c = \eta C \overline{\psi}^\textsf{T}$$

with $$C$$ an ordinary 4×4 matrix, having a form explicitly given in the article on gamma matrices. In conclusion, the 4-component Majorana equation can be written as

 * $$\begin{align}

0 &= \left(i\gamma^\mu \partial_\mu - m\mathsf{C}\right)\psi \\ &= i\gamma^\mu \partial_\mu \psi - m\psi^c \end{align}$$

Charge conjugation and parity
The charge conjugation operator appears directly in the 4-component version of the Majorana equation. When the spinor field is a charge conjugate of itself, that is, when $$\psi^c = \psi,$$ then the Majorana equation reduces to the Dirac equation, and any solution can be interpreted as describing an electrically neutral field. However, the charge conjugation operator has not one, but two distinct eigenstates, one of which is the ELKO spinor; it does not solve the Majorana equation, but rather, a sign-flipped version of it.

The charge conjugation operator $$\mathsf{C}$$ for a four-component spinor is defined as

 * $$\mathsf{C}\psi = \psi_c = \eta C\left(\overline \psi\right)^\textsf{T}$$

A general discussion of the physical interpretation of this operator in terms of electrical charge is given in the article on charge conjugation. Additional discussions are provided by Bjorken & Drell or Itzykson & Zuber. In more abstract terms, it is the spinorial equivalent of complex conjugation of the $$U(1)$$ coupling of the electromagnetic field. This can be seen as follows. If one has a single, real scalar field, it cannot couple to electromagnetism; however, a pair of real scalar fields, arranged as a complex number, can. For scalar fields, charge conjugation is the same as complex conjugation. The discrete symmetries of the $$U(1)$$ gauge theory follows from the "trivial" observation that

*: U(1) \to U(1)\quad e^{i\phi}\mapsto e^{-i\phi} $$ is an automorphism of $$U(1).$$ For spinorial fields, the situation is more confusing. Roughly speaking, however, one can say that the Majorana field is electrically neutral, and that taking an appropriate combination of two Majorana fields can be interpreted as a single electrically charged Dirac field. The charge conjugation operator given above corresponds to the automorphism of $$U(1).$$

In the above, $$C$$ is a 4×4 matrix, given in the article on the gamma matrices. Its explicit form is representation-dependent. The operator $$\mathsf{C}$$ cannot be written as a 4×4 matrix, as it is taking the complex conjugate of $$\psi$$, and complex conjugation cannot be achieved with a complex 4×4 matrix. It can be written as a real 8×8 matrix, presuming one also writes $$\psi$$ as a purely real 8-component spinor. Letting $$K$$ stand for complex conjugation, so that $$K(x + iy) = x - iy,$$ one can then write, for four-component spinors,
 * $$\mathsf{C} = -\eta \gamma^0 CK$$

It is not hard to show that $$\mathsf{C}^2 = 1$$ and that $$\mathsf{C}\gamma^\mu \mathsf{C} = -\gamma^\mu~.$$ It follows from the first identity that $$\mathsf{C}$$ has two eigenvalues, which may be written as
 * $$\mathsf{C}\psi^{(\pm)} = \pm \psi^{(\pm)}$$

The eigenvectors are readily found in the Weyl basis. From the above, in this basis, $$\mathsf{C}$$ is explicitly
 * $$\mathsf{C} = \begin{bmatrix} 0 & \eta \omega K \\ -\eta \omega K & 0 \end{bmatrix} $$

and thus
 * $$\psi^{(\pm)}_\text{Weyl} = \begin{pmatrix} \psi_{\rm L} \\ \mp\eta \omega\psi_{\rm L}^* \end{pmatrix}$$

Both eigenvectors are clearly solutions to the Majorana equation. However, only the positive eigenvector is a solution to the Dirac equation:
 * $$0 = \left(i\gamma^\mu \partial_\mu - m\mathsf{C}\right)\psi^{(+)} = \left(i\gamma^\mu \partial_\mu - m\right)\psi^{(+)}$$

The negative eigenvector "doesn't work", it has the incorrect sign on the Dirac mass term. It still solves the Klein–Gordon equation, however. The negative eigenvector is termed the ELKO spinor.

$$

Parity
Under parity, the left-handed spinors transform to right-handed spinors. The two eigenvectors of the charge conjugation operator, again in the Weyl basis, are
 * $$\psi^{(\pm)}_{\rm{R}, \text{Weyl}} = \begin{pmatrix} \pm \eta\omega\psi_{\rm R}^* \\ \psi_{\rm R} \end{pmatrix}$$

As before, both solve the four-component Majorana equation, but only one also solves the Dirac equation. This can be shown by constructing the parity-dual four-component equation. This takes the form
 * $$\beta \left(\delta_{\rm L} \oplus \mathrm{D}_{\rm R}\right) = i\gamma^\mu \partial_\mu + m\mathsf{C}$$

where
 * $$\delta_{\rm L} = i\overline{\sigma}^\mu \partial_\mu - \eta m\omega K$$

Given the two-component spinor $$\psi_{\rm R}$$ define its conjugate as $$\chi_{\rm L} = -\eta \omega\psi^*_{\rm R}.$$ It is not hard to show that $$\mathrm{D}_{\rm R} \psi_{\rm R} = -\eta\omega (\delta_{\rm L} \chi_{\rm L})$$ and that therefore, if $$\mathrm{D}_{\rm R} \psi_{\rm R} = 0$$ then also $$\delta_{\rm L} \chi_{\rm L} = 0$$ and therefore that

0 = \left(\delta_{\rm L} \oplus \mathrm{D}_{\rm R}\right) \left(\chi_{\rm L} \oplus \psi_{\rm R}\right) $$ or equivalently

0 = (i\gamma^\mu \partial_\mu + m\mathsf{C}) \begin{pmatrix} \chi_{\rm L} \\ \psi_{\rm R} \end{pmatrix} $$ This works, because $$\mathsf{C} (\chi_{\rm L} \oplus \psi_{\rm R} ) = -(\chi_{\rm L} \oplus \psi_{\rm R} )$$ and so this reduces to the Dirac equation for
 * $$\psi^{(-)}_{{\rm R}, \text{Weyl}} = \chi_{\rm L} \oplus \psi_{\rm R} = \begin{pmatrix} \chi_{\rm L}\\ \psi_{\rm R} \end{pmatrix} $$

To conclude, and reiterate, the Majorana equation is
 * $$0 = \left(i\gamma^\mu \partial_\mu - m\mathsf{C}\right)\psi = i\gamma^\mu \partial_\mu\psi - m\psi_c$$

It has four inequivalent, linearly independent solutions, $$\psi^{(\pm)}_{\rm L,R}.$$ Of these, only two are also solutions to the Dirac equation: namely $$\psi^{(+)}_{\rm L}$$ and $$\psi^{(-)}_{\rm R}~ .$$

Spin eigenstates
One convenient starting point for writing the solutions is to work in the rest frame way of the spinors. Writing the quantum Hamiltonian with the conventional sign convention $$H = i\partial_t$$ leads to the Majorana equation taking the form
 * $$i\partial_t \psi = -i\vec\alpha \cdot \nabla\psi + m\beta\psi_c$$

In the chiral (Weyl) basis, one has that
 * $$\gamma^0 = \beta = \begin{pmatrix} 0 & I \\ I & 0 \end{pmatrix},\quad \vec\alpha = \begin{pmatrix} \vec\sigma & 0 \\ 0 & -\vec\sigma \end{pmatrix}$$

with $$\vec\sigma$$ the Pauli vector. The sign convention here is consistent with the article gamma matrices. Plugging in the positive charge conjugation eigenstate $$\psi^{(+)}_\text{Weyl}$$ given above, one obtains an equation for the two-component spinor
 * $$i\partial_t \psi_{\rm L} = -i\vec\sigma\cdot\nabla \psi_{\rm L} + m(i\sigma_2 \psi_{\rm L}^*)$$

and likewise
 * $$i\partial_t (i\sigma_2 \psi_{\rm L}^*) = +i\vec\sigma\cdot\nabla (i\sigma_2 \psi_{\rm L}^*) + m\psi_{\rm L}$$

These two are in fact the same equation, which can be verified by noting that $$\sigma_2$$ yields the complex conjugate of the Pauli matrices:
 * $$\sigma_2 \left(\vec k \cdot \vec \sigma\right) \sigma_2 = -\vec k \cdot \vec \sigma^*.$$

The plane wave solutions can be developed for the energy-momentum $$\left(k_0, \vec k\right)$$ and are most easily stated in the rest frame. The spin-up rest-frame solution is
 * $$\psi_{\rm L}^{(u)} = \begin{pmatrix} e^{-imt} \\ e^{imt} \end{pmatrix}$$

while the spin-down solution is
 * $$\psi_{\rm L}^{(d)} = \begin{pmatrix} e^{imt} \\ -e^{-imt} \end{pmatrix}$$

That these are being correctly interpreted can be seen by re-expressing them in the Dirac basis, as Dirac spinors. In this case, they take the form
 * $$\psi^{(u)}_\text{Dirac} = \begin{bmatrix} e^{-imt} \\ 0 \\ 0 \\ -e^{imt} \end{bmatrix}$$

and
 * $$\psi^{(d)}_\text{Dirac} = \begin{bmatrix} 0 \\ e^{-imt} \\ - e^{imt} \\ 0 \end{bmatrix}$$

These are the rest-frame spinors. They can be seen as a linear combination of both the positive and the negative-energy solutions to the Dirac equation. These are the only two solutions; the Majorana equation has only two linearly independent solutions, unlike the Dirac equation, which has four. The doubling of the degrees of freedom of the Dirac equation can be ascribed to the Dirac spinors carrying charge.

Momentum eigenstates
In a general momentum frame, the Majorana spinor can be written as

Electric charge
The appearance of both $\psi$ and $\psi_c$  in the Majorana equation means that the field $\psi$  cannot be coupled to a charged electromagnetic field without violating charge conservation, since particles have the opposite charge to their own antiparticles. To satisfy this restriction, $\psi$ must be taken to be electrically neutral. This can be articulated in greater detail.

The Dirac equation can be written in a purely real form, when the gamma matrices are taken in the Majorana representation. The Dirac equation can then be written as
 * $$\left(-i\frac{\partial}{\partial t} -i\hat\alpha\cdot\nabla + \beta m\right)\psi = 0$$

with $$\hat\alpha$$ being purely real symmetric matrices, and $$\beta$$ being purely imaginary skew-symmetric. In this case, purely real solutions to the equation can be found; these are the Majorana spinors. Under the action of Lorentz transformations, these transform under the (purely real) spin group $$\operatorname{Spin}(1, 3).$$ This stands in contrast to the Dirac spinors, which are only covariant under the action of the complexified spin group $$\operatorname{Spin}^\mathbb{C}(1,3).$$ The interpretation is that complexified spin group encodes the electromagnetic potential, the real spin group does not.

This can also be stated in a different way: the Dirac equation, and the Dirac spinors contain a sufficient amount of gauge freedom to naturally encode electromagnetic interactions. This can be seen by noting that the electromagnetic potential can very simply be added to the Dirac equation without requiring any additional modifications or extensions to either the equation or the spinor. The location of this extra degree of freedom is pin-pointed by the charge conjugation operator, and the imposition of the Majorana constraint $\psi=\psi_c$ removes this extra degree of freedom. Once removed, there cannot be any coupling to the electromagnetic potential, ergo, the Majorana spinor is necessarily electrically neutral. An electromagnetic coupling can only be obtained by adding back in a complex-number-valued phase factor, and coupling this phase factor to the electromagnetic potential.

The above can be further sharpened by examining the situation in $$(p,q)$$ spatial dimensions. In this case, the complexified spin group $$\operatorname{Spin}^\mathbb{C}(p,q)$$ has a double covering by $$\operatorname{SO}(p, q)\times S^1$$ with $$S^1\cong U(1)$$ the circle. The implication is that $$\operatorname{SO}(p, q)$$ encodes the generalized Lorentz transformations (of course), while the circle can be identified with the $$\mathrm{U}(1)$$ action of the gauge group on electric charges. That is, the gauge-group action of the complexified spin group on a Dirac spinor can be split into a purely-real Lorentzian part, and an electromagnetic part. This can be further elaborated on non-flat (non-Minkowski-flat) spin manifolds. In this case, the Dirac operator acts on the spinor bundle. Decomposed into distinct terms, it includes the usual covariant derivative $$d + A.$$ The $$A$$ field can be seen to arise directly from the curvature of the complexified part of the spin bundle, in that the gauge transformations couple to the complexified part, and not the real-spinor part. That the $$A$$ field corresponds to the electromagnetic potential can be seen by noting that (for example) the square of the Dirac operator is the Laplacian plus the scalar curvature $$R$$ (of the underlying manifold that the spinor field sits on) plus the (electromagnetic) field strength $$F=dA.$$ For the Majorana case, one has only the Lorentz transformations acting on the Majorana spinor; the complexification plays no role. A detailed treatment of these topics can be found in Jost while the $$(p,q)=(1,3)$$ case is articulated in Bleeker. Unfortunately, neither text explicitly articulates the Majorana spinor in direct form.

Field quanta
The quanta of the Majorana equation allow for two classes of particles, a neutral particle and its neutral antiparticle. The frequently applied supplemental condition $\Psi=\Psi_c$ corresponds to the Majorana spinor.

Majorana particle
Particles corresponding to Majorana spinors are known as Majorana particles, due to the above self-conjugacy constraint. All the fermions included in the Standard Model have been excluded as Majorana fermions (since they have non-zero electric charge they cannot be antiparticles of themselves) with the exception of the neutrino (which is neutral).

Theoretically, the neutrino is a possible exception to this pattern. If so, neutrinoless double-beta decay, as well as a range of lepton-number violating meson and charged lepton decays, are possible. A number of experiments probing whether the neutrino is a Majorana particle are currently underway.

Additional reading

 * "Majorana Legacy in Contemporary Physics", Electronic Journal of Theoretical Physics (EJTP) Volume 3, Issue 10 (April 2006) Special issue for the Centenary of Ettore Majorana (1906-1938?). ISSN 1729-5254
 * Frank Wilczek, (2009) "Majorana returns", Nature Physics Vol. 5 pages 614–618.

title: Majorana equation


text:
Wikipedia:Articles for deletion/Yoism

 * The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or on a Votes for Undeletion nomination).  No further edits should be made to this page.

The result of the debate was Delete (Yes, I read the big essay at the end, sock/meatpuppet threshold exceeded, registered users deletes versus others show clear consensus. If you disagree, I would recommend VfU) Wikibofh 00:24, 22 October 2005 (UTC)
 * NOTE Wikibofh has explained his decision in greater detail here and I responded to his explanation in detail there.  Kriegman 23:57, 26 October 2005 (UTC)

Yoism
vanity. Only about 1 line of the article can be verified wikipedia is not a webhost Geni 20:34, 15 October 2005 (UTC)

Jeesis H. Kreist! Geni is a Yoan ;-) Damn!  Your "Homeopathy Sucks" page could be posted on our Yoism  site as an illustration of the difference between empiricism (the foundation of belief in Yoism) and false-beliefs.  Yoism is not a "religion" like what you probably assume it to be.  This underscores the problem caused by our web site being down.  Please see On Socks & Puppetfests, starting just below the votes. Kriegman 18:43, 19 October 2005 (UTC)

 * Strong delete. Note to admin closing this one: be sure to discount sock votes, as they are lots. -- (drini's page| ☎ ) 04:44, 18 October 2005 (UTC)
 * What's the reasoning behind your strong feeling? Are feelings without reasons how wikipedia works? -Orion

 * Another Note to Administrator Closing this one Please see a response to this "strong delete," On Socks & Puppetfests, starting just below the votes. Kriegman 18:43, 19 October 2005 (UTC)

 * Delete. A religious version of a micronation. None of the external links in the article work to verify claims. The "official" site states: "We've been hacked! Recently, Yoism has been getting a strong response from people all over the world." Right. Edwardian 21:51, 15 October 2005 (UTC)

 * Moved my comment to "Comment #1" on Talk page. Edwardian 19:01, 20 October 2005 (UTC)
 * Moved response to Edwardian's comment to Talk page.Kriegman 11:14, 21 October 2005 (UTC)
 * Moved my comment to "Comment #2" on Talk page. Edwardian 19:01, 20 October 2005 (UTC)
 * Moved response to Edwardian's comment to Talk page.Kriegman 11:14, 21 October 2005 (UTC)
 * Moved my comment to the "Comment #5" on Talk page. Edwardian 19:09, 18 October 2005 (UTC)
 * Moved response to Edwardian's comment to Talk page.Kriegman 11:14, 21 October 2005 (UTC)

[The following edit was placed after one of my responses to one of Edwardian's comment, which have been moved to the Talk page Kriegman 11:14, 21 October 2005 (UTC)]
 * alexa rank of 723,391. I'm not immpessed by your web site traffic.Geni 00:46, 17 October 2005 (UTC)
 * Hunh?! Not only shouldn't the degree that you are impressed by our web traffic be a standard for inclusion in Wikipedia, but what does this ranking mean?  If you noted, you didn't get a ranking for yoism.org.  For some reason, you got one for yoism.net (at least that is what I get when I go to Alexa).  Yoism.net doesn't even exist, and hasn't for many months.  Secondly, our Google hits went from around 9000 when searching for "yoism" a month ago to 770 today.  So, if this is a current ranking, and similar factors affect it as the Google hit number, despite the fact that it isn't even for yoism.org, what does it mean?  (If it is a delayed ranking based on six month to one year old data (which is what Alexa donates to public projects and goes back to a time when yoism.net may have existed), then that figure would be a fraction of what we were getting a few weeks ago.)  The traffic and interest I was referring to developed over this past summer.  Prior to that interest was steady but much lower.  But what ranking would we have to achieve to have a Yoism article in the Wikipedia?  Why is this relevant? Kriegman 01:24, 17 October 2005 (UTC)

 * It means that alexa thinks there are 723,390 websites that get more vists than your. In practice it means that you are off the bottem of the scale as far as alexa are concernded. The ranking are made up of the vists to yoism.org and twiki.yoism.org. The figure is the average for the last 3 months. However you look at your stats even your peak vists hardly show a strong world responce.Geni 01:44, 17 October 2005 (UTC)

 * You seem to be serious about this and may be trying to be impartial. Assuming you just didn't read the parts where I clarified what I meant by a strong response (after all this is getting lengthy), by "strong world response" I have now clarified that I meant that each day we were getting thousands of hits and about one (1, uno) response from a new person who showed an interest in pursuing Yoism further, and that our Google hits had grown from under 2000 to around 9000 in a few months.  Given the rate of growth we experienced in the past and that other religions experience early on, this was "a strong response."  That's all I meant by strong response on our redirected "We were hacked page."

 * In addition to 6 or 7 people showing some lasting interest each week, every couple of weeks we would get a threatening response from one or two people who were angered/threatened by our claims that traditional religions were misguided fantasies left over from humanity's childhood. I don't know who hacked our site.  But I suspected that it was no coincidence that our site was hacked shortly after we started getting thousands of hits along with such negative responses.  Rob, our new webmaster, thinks it was coincidence.  But this is what I meant on that redirected page by a strong world response, nothing more.  As far as I understand, the Alexa stats could be consistent with this, especially since the last three weeks have had zero or near zero hits on the yoism.org or twiki.yoism.org sites.Kriegman 04:54, 17 October 2005 (UTC)

 * Moved my comment to "Comment #3" on Talk page. Edwardian 19:01, 20 October 2005 (UTC)

 * Responses to Edwardian's Comment #3 have also been moved to talk page Kriegman 23:53, 21 October 2005 (UTC)

 * Moved my comment to "Comment #4" on Talk page. Edwardian 19:01, 20 October 2005 (UTC)

 * Do Not Delete. You can find some of the links to "verify claims" at http://web.archive.org/web/20040923210323re_/yoism.org/  Thank Yo for the WayBackMachine.

(Note: From the WayBackMachine FAQ:  "Why are there no recent archives in the Wayback Machine? We do not add pages less than 6 months after they are collected, because of the time delayed donation from Alexa. Updates can take up to 12 months in some cases."  Because of this, there are no Yoism pages archived from 2005.)

And indeed, "Right." In August and September, we were getting over 2,000 hits/day. That may not be much by some standards, but for us it was a very strong and steady response. We were getting emails from all over the world from people looking for Yoan meetings and/or interested in setting up chapters of Yoism other than in Boston, where it originated.

Our site, that has been up for four years nonstop, was, indeed, hacked by someone who began to send out spam using our dedicated webserver. Our webmaster closed down the site a few weeks ago even though it functioned fine and visitors would never know it was being used for spam! It is against Yoan principles to allow our server to be used for destructive purposes.

The problem was that we hadn't secured our site sufficiently against such hackers. Since securing it further would take expertise our webmaster hadn't developed, we decided to move it to a hosting service that would be responsible for security (instead of running our own dedicated server). The service we chose is www.gaiahost.net and we are setting up our site as I write. I set up the "We've been hacked" message on my personal web pages at my comcast account and had www.yoism.org traffic redirected to that page until we get our site back up. Meanwhile, for choosing to do the right thing---closing down our dedicated server that was being used for nefarioius purposes, instead of letting it run while we set up our new site---the article about Yoism is being proposed for deletion.

Furthermore, there was extensive discussion of deletion when the Yoism article was first created. After a great deal of debate and modification of the article in 2003 the issue was apparently settled.

I hope this clarifies the apparent problem with the article. I hope it seems reasonable to wait a few weeks to see what the links refer to when the Yoism site is back up. Or if it is necessary, I can recreate the specific pages (except our home page which is too complex for me) that the Yoism article links to at the same Comcast site where the "We were hacked" message is hosted.

In the meantime, I would propose that the article be removed from pages for deletion and the banner removed from the article. Kriegman 02:25, 16 October 2005 (UTC)

The link in the Yoism article to the external Yoism page containing an article about Yoism that appeared in the Boston Globe obviously doesn't work because the site is down. However, the article can be accessed in the Boston Globe's archives. Kriegman 02:41, 16 October 2005 (UTC) [Later, in response to one of Edwardian's comments, which is now on the Talk page, I wrote, "Though I would rather have spent my energy on getting our website back up and not on creating a temporary repository of pages to "relitigate" the issues debated at length in 2003, you can now view the full Boston Globe article here."]Kriegman 11:14, 21 October 2005 (UTC)

 * Do Not Delete. Hello -

As someone who was active in the Yoan community for a number of years (starting in 1998), I can assure you that it in no ways resembles the "micronations" you describe (defined in Wikipedia as "entities that resemble independent nations or states, but for the most part exist only on paper, on the Internet, or in the minds of their creators.") The Yoan community was an actual group of people who met weekly at gatherings in Somerville and Cambridge, Massachusetts, many of which I attended. Its participants was crucially active in volunteer efforts for a nonprofit project for human rights in mental health located in Whitman, Massachusetts. Furthermore, the ideas of Yoism have provided the basis for vibrant discussions about the nature of religion and truth for not only its immediate members, but many others around the world by way of the internet. These discussions continue today from far corners of the planet.

Knowing first-hand the webmaster of the Yoism web site, I can verify that their server indeed been hijacked recently and is undergoing security improvements.

Whether or not the links listed on Wikipedia are currently inactive or not, Yoism is alive and well as a concept in the world, and I strongly object to the article being removed.

Sincerely, R. Hull

 * Do Not Delete. Hi. I know that Yoism is still active. Their website was hacked. Their wiki entry should not be deleted. Thank you.

B. Miller

 * Do Not Delete. I know the people in charge of yoism.org, and so I know that the server was hacked around the beginning of October and is currently being restored.  Therefore deleting the page for the reasons suggested (e.g. that the links do not work) would be a bad decision.  ToddDeLuca 16:02, 16 October 2005 (UTC)

 * no previous edits to wikipedia.Geni 13:35, 16 October 2005 (UTC)

 * Do Not Delete24.60.21.122 18:19, 19 October 2005 (UTC). Likewise, I have been involved with Yo for a while.  I'm the person working on setting up the web page again.  I spoke to Dan in person just hours after the hacking occurred.  Zac was able to reestablish the page, but the offenders who had gained accessed we soon learned were using the server for sending spam.  We had no other choice but to shut down the server.  If you ask me, the reason why we were attacked has absolutely nothing to do with ideology or religious contentiousness-- it's because our server had lousy security and some industrious hacker exploited that for their own selfish purposes.  I think Yo is a significant enough to warrant having a wikipedia entry.

NOTE: For readability purposes I also tagged Brendan Miller's, Rich Hull's, and Dan K.'s posts with "do not delete" because this page is for voting and they are clearly voting by posting these comments on this page. I wanted to make this clearer by putting the uniform heading on their entries.

But I want to know: what counts as vanity? What is the criterion for something being worthy of inclusion? Admittedly it is a relatively small thing at this point. But why should wikipedia rule out inclusion of smaller scale phenomena? If there is such a rule (for example a rock band on a tiny record label that is only known in non-commercial contexts and small distribution magazines does not exist but a rock band that is featured in big time magazines does exist) than what is the actual criterion for scale-- and why ever should wikipedia be against grassroots non-commercial culture??

Rob    [Note this user (24.60.21.122) has numerous, unrelated, prior edits. Kriegman 20:20, 19 October 2005 (UTC)]

 * WP:MUSICGeni 17:11, 16 October 2005 (UTC)

 * Delete as non-notable. We don't have specific criteria for religions, I think we should, but existing for only ten years and having only 100 members would no doubt be below them. Wikipedia is not used for groups to establish themselves, it is for describing groups already sufficiently notable. -- Kjkolb 09:09, 16 October 2005 (UTC)
 * Response to Kjkolb: After modifying the article greatly in response to NPOV and presenting independent evidence of Yoism's existence, this became the sole and main issue in the lengthy discussion that occurred in 2003. Given that paper space is not an issue in the Wikipedia, the issue of number of members or notoriety need not be considered rigidly in establishing a Wikipedia article.  Membership in a religion is a rather large step and for every person that joins/identifies as a member of a religion there are hundreds who are aware of it.  Indeed, there are thousands of people who have engaged in discussions of Yoism, much of which can be found in Google searches.  Having 100 participants in the Boston area was deemed sufficient in 2003.  Since then the number has grown with most of that growth occurring outside of Boston and being impossible to count.  We have received numerous emails that begin something like, "I have considered myself a Yoist for years now and was wondering . . ." from people we have never heard from before.  I believe a legitimate claim could be made that the number of Yoans easily exceeds 1,000.  But I have not edited the Wikipedia article with the more accurate new numbers  because I had no external source with which to verify them.  Despite wanting to change the numbers (nothing makes something more popular than seeing it become popular with other people), I have become more of a Wikipedian since 2003 and, beyond understanding the rules, without some independent reference I didn't even consider such a revision possible.  I figured that that can wait until there is some other independent source for the new numbers.  I never thought, that after more than doubling in size, we would have to re-debate the size issue or see the Wikipedia article deleted.  Kriegman 14:12, 16 October 2005 (UTC)

 * Another point to add, there is no way possible that inclusion in the Wikipedia could mislead a reader into thinking that Yoism is more substantial a phenomenon than it is. The reader is presented at the very beginning with a statement (actually an understatement, but that just reinforces this point) about the size of membership.  I believe that was put into the article up front back in 2003 for precisely this reason, i.e., to make sure that inclusion in the Wikipedia did not suggest something about the magnitude of this phenomenon that was not so.

 * I think it is presumptuous to then suggest that around phenomenon where signficance based on sufficient size is debatable, if presented with the necessary information, readers cannot evaluate the importance of the phenomena for themselves. If presented with the information for an accurate picture of this issue, I see no need to protect readers form being exposed to information that some people feel is of insufficient importance while others disagree (as was well established in 2003).  Nobody is being misled.  Furthermore, the article has existed with these low numbers being presented up front for over two years.  Clearly readers of this article have not felt that the numbers issue was a sufficient problem to make an issue of it, until the links stopped working and some erroneous assumptions were made about what the temporary redirect of those links indicated about Yoism.

 * And many, many people have found the article to be of importance; it is often cited as a reason for their further investigation of Yoism. Despite the fact that this last point is of interest to me as one who wants to see Yoism spread, consider that fact carefully:  After being told that there are 100 or so participants in Yoism (understatement or not), numerous individuals have found the information in the article to be of sufficient siginificance to spend their time investigating Yoism further.  If you accept the fact that this has occurred (and while I acknowledge that I have not proved it, if you don't believe me, then just consider this a hypothetical illustration [a thought experiment] of why a specific numerical definition may be misleading), I think this would be evidence that the "size" issue should not be set according to some subjective notion that doesn't match real world behavior in which people are finding the description of this phenomenon to be of sufficient significance to spend their own life energy in researching further.  Surely, that would be evidence of more significance than many, many Wikipedia articles.

 * Finally, regarding the 10 year figure as insufficient. Why would religious phenomena need to exist longer than other cultural phenomena before they can be included in the Wikipedia?  If we had a ten year rule (or even a five year rule, or even a two year rule) for sociocultural phenomena, many thousands of Wikipedia articles would have to be deleted.  There are an enormous number of cultural phenomena that---especially in our information age---achieve significance in far less than 10 years.  Consider for example, Wikipedia. Kriegman 14:57, 16 October 2005 (UTC)

 * Do Not Delete.

I see no need for deletion. If they have been active since 1998 and got abused by criminal hackers then I get that some of you find the page confusing. I say wait wait at least until they set up the new server so everybody commenting could do it on the real thing. Compared to many other texts Yoism belong here. I would feel let down if wiki didn't have the text it has now. I saw it as very informative. It is no hoax at all.

BernieDaSwede BernieDaSwede 18:27, 16 October 2005 (UTC)

 * user's first edit.Geni 13:25, 16 October 2005 (UTC)

 * Do Not Delete.

Considering we've already had this discussion a few years back and decided not to delete, and considering there are at least a couple news paper articles about Yoism (indicating that people do find it relavent), I think this is a pretty clear case. It relevant. People find it interesting. It doesn't detract from the rest of the Wikipedia in anyway. Its only a net positive, and it has been cited a few times in paper media, so it belongs.

OverZealousFan 15:55, 16 October 2005 (UTC)

 * you appear to only have 3 edits not directly related to Yoism.Geni 23:59, 16 October 2005 (UTC)

 * Do Not Delete.

I see no good reason for deletion. Yoism is a real phenomenon whose website is down temporarily. It would be a shame to lose it in the wikipedia.

WikiMe 17:31, 16 October 2005 (UTC)

 * user's first contibution to wikipedia.Geni 18:19, 16 October 2005 (UTC)

 * Delete

I don't think the website being down matters at all. The yoism website is still not a source other than Dan Kriegman, its just another vehicle for him. Why should Wikipedia be the sole supporter and host of this religious philosophy? This has nothing to do with knowledge, just advertising and proselytizing. Dan Kriegman needs to pay for his own commercial airtime. (Kriegman's already told us he has incorporated and can legally receive moneys from supporters...) It seems to me any Yoism page on Wiki should be focused on the way the "group" is trying to expand, by exploiting the "open source" philosophy of Wikipedia *specifically* - this is the only thing we really know these "Yoans" are actually doing. PilgrimZ 21:21, 16 October 2005 (UTC)

 * User has no previous edits to wikipediaGeni 23:59, 16 October 2005 (UTC)

 * Do Not Delete. The first commonet on the first vote here is from someone thinks this article should be deleted because Yoism sounds like it might be a "micronation". Yet the Wikipedia entry for micronation has over a dozen references to micronation entries in Wikipedia itself.  Even if Yoism were one (its not) this is no good reason to delete the entry. I have been following Yoism for over a year and the main Yoism website has been up all that time, and it has a very active following on its mailing list. 64.142.28.232 21:46, 16 October 2005 (UTC)

 * we generaly don't accept votes from IPs.Geni 23:59, 16 October 2005 (UTC)
 * The Articles for Deletion page states, that recommendations by "Unregistered and new users . . . may be discounted, especially if they seem to be made in bad faith (for example, if they misrepresent their reasons)." No one has suggested that anyone has misrepresented their reasons or acted in bad faith.  And those who have been participants in Yoism, have been quite up front about it.  This particular user made at least one unrelated Wikipedia edit before the Yoism article was put on the AfD page. Kriegman 18:35, 17 October 2005 (UTC)

Do Not Delete

If somebody hacking a website all of a sudden makes something not exist, then Wikipedia is in a sad state of affairs. I am a Yoan and have been involved with them for some time. You should be able to see from previous discussions of whether or not Yoism's wikipedia entry should stay or go (when the site was up and running) that this bridge has already been crossed and it was decided that it should stay.

Wikipedia defines religion as " In its broadest sense some have defined it as the sum total of answers given to explain humankind's relationship with the universe." So regardless of how few follow the faith, it's existence (which is clear from the people voting for it to stay) and differentiation from any other faith means that it should stay as it adds to the encyclopedic knowledge of religion.

You know Christianity was once a cult as well. If you would like more information about the existence of Yoism you can check [here], the australian branch of the religion which is currently still under web development (as there are currently only 2 Australian Yoans)

Igdrasa

 * User has two previous edits to wikipediaGeni 23:59, 16 October 2005 (UTC)

 * Delete nn, puppetfest. Xoloz 12:29, 17 October 2005 (UTC)
 * "Puppetfest" put into search doesn't return anything. If by "puppetfest" you mean sock puppets, I believe you are wrong.   [To Xoloz:  This is the kind of misinformation that red staters are prone to use ;-)  From your writing, you seem very Yoan.  Angry, but Yoan.  BTW, I think Louis Black would do a great job of reading your fts.com page.] Kriegman 14:33, 17 October 2005 (UTC)

I've edited a few wikipdedia articles from different IP addresses (mainly in the topic of Global Governance, Global Democracy, Global Citizens, etc), but admittedly have not been very involved (although, I probably will become more involved over time). I am a Yoan. The article on Yoism clearly promotes Yoism, but it is also an article in good faith reporting a newish phenomena re: a specific Open Source Religion. Yoism is real, the number of Yoans uncounted but an estimate of 1,000 or so seems plausible. It is an independently verified group (definitely not a micronation, definitely in existence beyond Dan Kriegman and the website). I understand the concerns Wikipedians have about the misuse of wikipedia, and I understand the requirements for no new research, NPOV, no micronations, etc. -- to be a resepcted and established source of information it is important to take these concerns very seriously. Wikipedia is under attack by academics and others for being too loose in its criteria of inclusion, yet the backlash effect of this attack is stressful and annoying on the open source culture. Articles exist because of interest in them, this is true on all topics, and they evolve over time by the participation of many people from around the world -- i.e., they improve continuously (this is what makes Wikipedia special--a bad article, of which there are many, is most often simply a new article remaining to be edited, other encycolpedia publish only edited version, so those who critique wikipedia on this point are simply ignorant of the process). Anyhow, imho, wikipedians should have more confidence in the validity of their project, its methods, and principles -- and it would betray all of these to delete the Yoism page. Orion Kriegman OrionK 18:19, 18 October 2005 (UTC)
 * Do Not Delete.

I am not a Yoan -- and wouldn't be because of their hot-under-the-collar anti-monotheism -- but I find their idea fascinating and much of their work very creative. I think they are modelling something -- the co-creation of religious ideas and rituals -- that is useful for all of us to consider. It is too bad that their site has been taken down temporarily. While it was up, I spent several hours exploring it, and am discussing the collaborative formation of religions now with some other people, in other contexts. The fact that Yoism arose out of the cooperative movement fascinates me. I now use Wiki as my default source for looking up things (even before Google half the time), and I would be very disappointed if because something is new, it was dropped from the Wikipedia regardless of how substantive it is. Wikipedia is not a stale record of the past, but a living representation of reality as it is emerging. Please keep it that way. -- Tom Atlee, Author of The Tao of Democracy
 * Do Not Delete
 * Links to Atlee article and book added by Kriegman 04:21, 20 October 2005 (UTC)

 * Delete but keep in some form also.  Molotov   (talk)  [[Image:Flag of California.svg|25px]]   21:35, 17 October 2005 (UTC)

 * Keep Disinterested third-party here who stumbled across this article after seeing it linked to Timothy Leary and was very surprised to see it listed on AfD. I found it to be pretty well written and certainly informative and encyclopedic (verifiable, notable, etc.) I understand, per the nomination, that it was originally just a one-line article, but since then, it has been expanded significantly, a very nice side-effect of the AfD process. Please keep! --Presnell 18:23, 18 October 2005 (UTC)

 * Umm no the article was always that size. There is almost nothing verifiable about the group beyond there being at least 30 of them (even that isn't going to break any records as the most verifiable claim ever)and being registered with the IRS.It just isn't posible to write a NPOV article about them.Geni 18:18, 20 October 2005 (UTC)
 * This is not a fair representation of reality. When a church has attendance of 30 (which is what was reported in the Boston Globe article), is the membership likely to be 30?  And, of course, sarcasm aside, we don't need to break verifiability records to be in the Wikipedia.  And experienced Wikipedians, who had access to our temporarily down web site two years ago, did feel a NPOV article could be written about Yoism.  And they mostly rewrote it to make sure it was NPOV!  (Also see the "On Socks and Puppetfests" discussion below for a further basis for a valid article.) Kriegman 19:53, 20 October 2005 (UTC)

 * Non-Profit status, as indicated by the 501(c)(3) approval, and contemporary news reports provide enough verifiability and notability for me, at least, to request that this article should not be deleted. Again, I'd never heard of this movement until I came across the wikipedia article, and I found it informative and interesting. --Presnell 17:01, 21 October 2005 (UTC)

 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in an undeletion request). No further edits should be made to this page.

 * The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or on a Votes for Undeletion nomination).  No further edits should be made to this page.

The result of the debate was Delete (was part of one above, the formatting messed it up) Wikibofh 16:02, 22 October 2005 (UTC)

On Socks & Puppetfests: Another "note to administrator closing this one"
There is a claim that there are sock puppets in this discussion and that the votes of folks with no or few previous edits should be discarded. There are two separate issues raised by this: (1) are they sock puppets and (2) if not, should their votes be treated as such under the meat puppet extension to the sock puppet rule.

 * Sock Puppets

To address the first issue we can look at the official "sock puppet" policy, which states:
 * If it appears that sock puppets are being used as part of an edit war or to distort the outcome of a vote or survey, one possible rule of thumb is the 100-edit guideline. This suggests that any account with more than 100 edits is presumed not to be a sock puppet. If there are unusually many accounts with few edits participating, you may want to check if they are sockpuppets, by looking at IP addresses or times that edits were made. However, simply having made few edits is not evidence of sockpuppetry on its own, and if you call a new user a sockpuppet without justification, they will probably be insulted and get a negative impression of Wikipedia.

 * Keep in mind there can be multiple users who are driven to start participating in Wikipedia for the same reason, particularly in controversial areas such as articles about the conflict in the Middle East, cult figures, or Wikipedia:Articles for deletion. Some have suggested applying the 100-edit guideline more strongly in such cases, assuming that all accounts with fewer than 100 edits are sock puppets. Generally, such beliefs have been shown not to be well founded.

 * If there is doubt, a developer can easily check to see whether accounts are related. Experience has shown that on article talk pages, including polls, the linkage is usually not supported by the information available to developers, so self-restraint in making such accusations is usually the right course.

So, the rule advocates caution and points out that the assumption of sock puppetry is usually wrong. Yet two very experienced Wikipedians have suggested sock puppetry is rampant here (and/or that we are dealing with meat puppets, discussed below) and have issued delete votes with no sign they they engaged in any close consideration of this particular vote (and, I admit, no sign of a lack of such either, just a "quick" vote).

I can assure the administrator closing this that there are few, if any sock puppets involved on the "do not delete" side. This is NOT because I know all or most of the do not deleters. It is because the do not deleters who are first timers or have few edits and have a vested interest in Yoism have either (1) used their real names (and could thus be contacted to verify their identities and votes) or (2) self-identified themselves as Yoans and/or as people who know Yoans and have some relationship with them. This latter action would totally undermine any gain sought by sock puppetry.

In addition, some votes can be counted as evidence from real people even if their vote may be discounted relative to more active Wikipedians. While statements from Rich Hull, B Miller, and Todd DeLuca may not be considered authoritative enough to support an article or a statement in an article, in this case they can be used for something else. They are evidence that the fact that "our site is down" is not some bogus claim for a non-existent phenomenon. Actually, they serve as reminders that there is another source of verification of this: two years ago in a similar process, concerned Wikipedians repeatedly visited our web site and then suggested changes to the article to make it NPOV, to limit its claims (one of them edited the article to make sure it noted the small known number of active Yoans at the very beginning), and to suggest specific verification that could be added to the article (like the incorporation documents as the more authoritative 501(c)(3) status didn't exist then).

The vote from Tom Atlee, provides evidence (that can be verified because he has identified himself) of the utility of the article from a real non-Yoan who is a regular user of the Wikipedia. I know of many others who have found the article useful in that way, but Tom Atlee's vote is independent evidence of such. I don't know how often you have such information in a VfD process and so there may be no "official policy" about how to use it. But surely it should not be ignored.

But in some cases, when there are no or very few previous edits, we could be dealing with meat puppets. So let's turn to that issue.

 * Cursory votes from experienced Wikipedians versus possible meat puppets

Obviously, votes can be stacked by a call to a community of non-Wikipedians to participate in a Wikipedia vote. So, there is a reason to discount first time participants and to weigh the votes of experienced Wikipedians more strongly than those who have made very few edits. There are two things to consider in this regard when looking at this particular vote.

First, part of the reasoning for applying this rule when there are at least some other unrelated prior edits by the voter is to counter the sock puppet possibility. In this case, where genuine sock puppetry is probably minor to nonexistent, I think this concern should be disregarded and we should only be concerned with meat puppets. So, in the cases of users who made at least one unrelated edit prior to this VfD, it would be unreasonable to ignore their votes (as they are unlikely to be sock puppets) and the question remains should they be discounted relative to the votes of experienced Wikipedians.

I believe there is also a strong reason to be careful about invoking this aspect of policy, and/or to temper the degree to which it is used. If you look at the earlier vote two years ago, the VfD process resulted in numerous editing changes to the article. In the course of the VfD, numerous non-Yoan Wikipedians went to the web site to see what this Yoism thing is. They came back to the discussion and suggested and made changes to the Yoism article. Ultimately, it was decided to keep it.

Why is this important? It is important because there is another standard at play in almost every Wikipedia article about topics that are not subject to careful debate and publication in peer review journals. Some artiicles are allowed to stand on this other standard alone that may include no reference whatsoever to printed articles in authoritative sources. Other articles include large segments that stand on this other standard alone. And most articles have some segments that are only based on this standard.

 * Face validity: The "Apple Pie" standard found in, at least, segments of many, if not most, Wikipedia articles

By "face validity," I mean "when an article makes descriptive claims that are easily verifiable by any reasonable adult" (taken from the No Original Research policy). This standard is invoked when editors look at a phenomenon directly and see if the article reflects it accurately. Indeed, face validity is always employed. And this is true even when references from peer reviewed research are the basis for the article: different editors can then go and look at the peer reviewed publication and see if the description in the Wikipedia article comports with it. That is, all Wikipedia articles are ultimately based on "convergent face validity," i.e., wording that converges on an agreed upon description of some phenomenon outside of the Wikipedia that editors each experience directly. When there is peer reviewed research, convergent face validity is the standard by which the article is judged to accurately reflect that research. When there is only convergent face validity---i.e., the apple pie standard "when an article makes descriptive claims that are easily verifiable by any reasonable adult"---editors ensure that the article comports with what they as a group have directly experienced and, by logical extension, assume that "any reasonable adult" could also verify.

In applying face validity---whether there are external publications to support the article (and the face validity is used to judge whether the article accurately desciribes what can be found there) or when only the face validity of the apple pie standard is in play---the editors must always be able to directly experience some external phenomenon and then edit an article so that the words comport with their collective experience of the external phenomenon.

In addition to whatever publications may be referenced to support an article, I would suggest that many if not most legitimate Wikipedia articles are at least partly dependent on the apple pie standard. For one example, consider the many South Park articles, where you can easily spot thousands of theories/beliefs/statements that are unsubstantiated by any references beyond the editors' opinions (and it may be ages before there are published references addressing more than a handful of these cultural theories/beliefs). Here are five examples, taken from one small section of the main South Park article):

 * Cartman is "often the funniest" (I agree.)
 * Kyle is the "most easily persuadable" (Most easily of who? Certainly not Butters.)
 * Butters is "repressed by his overbearing and oppressive parents" (I agree)
 * Barbrady is "incompetent" (I agree)
 * Satan is "insecure" (I agree)

But, some people would claim, my agreement (or yours, or other editors) is not to be the measure of whether a claim should be in the article; that's "the Sin of Original Research" (pun intended). After all, we are only editors. But where will you find "peer reviewed" articles to support the zillions of such cultural claims/judgments/descriptions that can be found in these articles? Nowhere. The idiosyncratic inaccuracies in such claims are corrected by other editors based on their examination of the evidence (i.e., their experience viewing South Park).

Now some of the specific statements above can probably actually be found in published external works. Yet the South Park articles are filled with many thousands of such claims, the vast majority of which have not been verified and will never be verified by specific citations in published works. It is simply clear that despite the fact that South Park has a healty "External links" section, not more than a tiny, tiny fraction of the thousands of specific claims made in the main and related South Park articles can be verified by its external links.

It is the face validity of these innumerable, unreferenced claims that can be and ultimately is judged by the Apple Pie standard, i.e., easily discernable, community agreement about the face validity of the statements or what any reasonable adult can verify by, in this case, watching South Park. Indeed, I edited one of the descriptions of an aspect of South Park using my judgment and participated in the process of moving the article's descriptions closer and closer to one the community of editors can agree on and thus what a "reasonable adult could be expected to be able to verify." It is not my judgment (which would be original research) that is the standard, but rather the face validity that is established by the judgments of many editors input that ensure that the wording "evolves" into something agreed upon, and is thus likely to be something that could be verified by any reasonable adult.

 * Back to Yoism

One of the reasons that deletion was suggested for the Yoism article two years ago was that some editors thought it might be a hoax or a joke. Editors then went to the Yoism website and easily discerned that it was not a hoax or joke (though some may have found it to be laughable, that's not the point). That is, they were able to use face validity to ensure that any reasonable adult could verify that it was not a hoax or a joke and thus eliminated that concern.

This is the point. They were able to determine directly that any reasonable adult could be expected to verify that Yoism is a fairly well developed religious belief system that has undergone considerable development and is sufficiently different enough from other religions to demonstrate the existence of a phenomenon that may be of interest to Wikipedia readers. They still insisted on having some independent basis upon which to conclude that the phenomenon described in the article was not simply vanity and that it existed in the awareness of a discernable segment of the human population, not just in the Wikipedia. They got this from the incorporation documents, eventually from the Boston Globe article, and, in part, from the web site itself, which referenced events that had occurred in specific locations and times, such as meetings and presentations at Brown University (which was also documented in the Globe article in the interview segment with Rich Hull).

Thus, the article was kept because there was a combination of external verification AND apple pie face validity of the phenomenon. This combination is employed, in part, in almost all Wikipedia articles that are not about topics that are typically researched and/or described in print publications or topics for which that process has just begun, including many new cultural developments affecting only a subsection of society.

In this regard, please reconsider the "cursory" votes of the experienced Wikipedians versus those who have made fewer edits. Though some do not delete votes come from fairly experienced Wikipedians, a few highly experienced Wikipedians have voted for deletion. Yet, none of those highly experienced voters have had the ability to visit the web site and see what the phenomenon described briefly in the artilce refers to. All of the Wikipedians---including non-Yoans---who have voted on this page to keep the article have done so. I am suggesting that an important source of a type of external verification (of the apple pie sort) was available to all Wikipedians two years ago (albeit in a more primitive form) and is currently temporarily unavailable because of the activity of a hacker.

This leads me back to my original concern: that this repeat VfD process was not deemed necessary for two years until shortly after our site went down and the ability to take a closer look at what Yoism is was missing. That is, regardless of the limited nature of the external verification, others who came across our article could easily verify that Yoism:

 * has significant (though limited) external validation including at least: incorporation, an independent article in a major newspaper, 501(c)(3) status that requires rigorous extensive documentation (and did not exist two years ago), and (up until the hacker caused us to close our site) a significant web presence of many thousands of hits in response to a Google search
 * has a well-developed religious belief system that has undergone considerable development
 * is sufficiently different enough from other religions to demonstrate the existence of a phenomenon that may be of interest to Wikipedia readers

Given the current context, the unexplained, brief (which is what I mean by "quick" or cursory) deletion votes by very experienced Wikipedians should be seen in the light that they could not employ this very simple process to add any face validity apple pie to their decision. Would they have visited our web site if they could? I would hope they would have a least taken a brief peek. But one thing we do know: When the web site was available and we went through this process before, the experienced Wikipedians did take a look and were satisfied that there was something there. When experienced Wikipedians could visit our site PLUS they could examine some external evidence (now with the 501(c)(3) status and a much more signficant web presence that should account for at least something) they reached a decision to keep.

In Summary

When counting or discounting votes based on experience, please keep in mind that all of the votes to delete (including those by a few very experienced Wikipedians) were made without benefit of the data that, two years ago led experienced Wikipedians to a decision to keep. Thus, we must bear in mind the following two points (which are true as the five day period for this VfD nears an end):

One: All (100%) of the "Delete" votes that come from folks with ANY edits, come from folks with more than 2,000 edits, and these same folks are also folks who have never visited the web site that was a crucial factor in the decision to keep made two years ago, which also involved experienced Wikipedians.

Two: Wikipedia administrators and folks with over 2,000 edits are not your average Wikipedia user or even your average Wikipedian. Though administrators are a varied lot and often disagree about many things, there must be ways in which such a high level of commitment and participation introduces some bias into what an encyclopedia should be. And surely, as an open source enclyclopedia for the world, input from non-editor users and editors who are not highly involved editors of the administrator degree must not be ignored. In this VfD, all (100%) of the votes that come from editors with at least one and less than 2000 PRIOR, UNRELATED edits are "Do Not Delete."

Based on these facts, a final decision to delete would mean that, even if you are an editor, if you do not have a huge number of prior edits---even if you have access to information that those with more than 2,000 edits do not have and which, in the past, Wikipedians much more experienced than you found to be important in making this decision, and even if you spell out your reasoning in detail---your vote may be ignored in favor of the votes of super-experienced users who give little or no justification for their votes (other than invoking a rule), and thus showed no sign of careful investigation of this particular article. It would be a message that we have created a new elite in which only those with an extraordinarily high level of participation will have their voices heard in what is ostensibly an open source project that invites all users to participate.Kriegman 17:55, 20 October 2005 (UTC)

 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in an undeletion request). No further edits should be made to this page.

title: Wikipedia:Articles for deletion/Yoism


text:
User talk:Cvereide

Welcome
Hello, , and welcome to Wikipedia. Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers: I hope you enjoy editing here and being a Wikipedian! By the way, you can sign your name on Talk and vote pages using three tildes, like this: ~~~. Four tildes (~~~~) produces your name and the current date. If you have any questions, see the help pages, add a question to the village pump or ask me on my talk page. Again, welcome!}} -- Psy guy (talk) 20:34, 15 October 2005 (UTC)
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Associated Food Stores

Associated Food Stores is an American retailers cooperative that supplies nearly 450 independently owned retail supermarkets throughout Utah, Arizona, Idaho, Colorado, Montana, Oregon, Nevada, and Wyoming.

Description
The headquarters for Associated Foods is located at 1850 W 2100 South in Salt Lake City, Utah, United States. The company's president and CEO is David Rice. He replaced Bob Obray following Bob's passing in August 2022. It reported over US$1.6 billion (equivalent to $ billion in ) in sales during fiscal year 2007 and is currently the fifty-sixth largest grocery retailer in the country by volume with 23% of its total sales coming from its corporate stores.

History
Associated Food Stores was founded in 1940 by Donald P. Lloyd, president of the Utah Retail Grocers Association along with 34 Utah retailers. Concerned with the effect that large corporate stores would have on small independent retailers, he felt the only way these small businesses could survive is if they united and faced the competition as one, therefore increasing their collective buying power. He convinced 34 stores to donate $300 (equivalent to $ in ) to help build an independent and "associated" warehouse.

In 1999, Associated Food Stores purchased Utah grocery store chain Macey's. In August 2017, Macey's broke with 70-year tradition by deciding to open some of their stores on Sundays.

In 2009, Associated Food Stores purchased 34 Albertsons stores in Utah from Supervalu Inc. The stores were renamed Associated Fresh Market (more commonly known as just "Fresh Market"). As of June 2017, however, only 17 of the originally purchased locations were still under the Fresh Market banner, the rest having been either closed or sold.

In 2017, two Fresh Market locations in Murray and Holladay were re-branded as Macey's.

As of 2021, three Macey's locations have closed: the Logan (400 North), Clinton, and the Midvale/Sandy locations.

In 2022, a former Fresh Market in American Fork became a Macey's.

Corporate stores
As well as supplying independent grocers, Associated Food Stores also owns several corporate stores under five different names, operating a total of 38 locations.
 * Macey's is their largest brand, and has 17 locations across the Wasatch Front, Tooele, and the Logan area.
 * Here are the locations, all are in Utah:
 * Draper
 * Logan/Providence
 * Ogden
 * Taylorsville
 * West Valley City - Granger
 * SLC - Parleys Way
 * SLC - Mount Olympus
 * Holladay
 * West Jordan
 * Orem
 * Highland
 * Lehi
 * Pleasant Grove
 * Provo
 * Spanish Fork
 * Santaquin
 * American Fork
 * Murray
 * Tooele
 * Eagle Mountain
 * Fresh Market was created after their acquisition of most of the Albertsons locations in Utah. There are currently only two Albertsons left in Utah, which are in Washington and Saint George. There are currently 10 locations along the Wasatch Front and in Park City. This is significantly fewer than the 34 locations they originally purchased from Albertsons.
 * Their locations
 * Park City (Deer Valley Drive)
 * Park City (Kilby Road)
 * Ogden
 * South Ogden
 * Layton
 * SLC (900 East)
 * SLC (2300 East)
 * Provo
 * Lin's has 7 locations in St. George, Hurricane, Cedar City, Richfield, Price, and Overton, Nevada.
 * Dan's has 2 locations in Salt Lake County. The locations are in Cottonwood Heights and SLC. Two former Salt Lake City locations have closed, one was replaced by a JoAnn, and the other was replaced by a Macey's.
 * Dick's Market has 2 locations in Davis County. They're located in Bountiful and Centerville.

Other stores

Popular stores owned and/or supplied by Associated Food Stores:

 * Broulim's (Idaho, & Wyoming)
 * Clark's Market (Arizona, Colorado, and Utah)
 * Dan's Market (Utah)
 * Dick's Market (Utah)
 * Finley's Food Farm (Montana)
 * Fresh Market (Utah)
 * Harmons (Utah)
 * Kent's Market (4 locations, Utah)
 * Lee's Marketplace (7 locations Utah)
 * Lin's Market (7 locations)
 * Macey's (Utah)
 * Peterson's Fresh Market (Utah)
 * Raine's Market (Nevada)
 * Reams (Utah)
 * Soelberg's Market (Utah)
 * Ridley's Family Markets (3 locations, Utah)
 * Winegar's Market (Utah)
 * Stokes Market (Utah & Idaho)

Western Family
Associated Food Stores was a primary distributor of the popular store brand Western Family owned by Western Family Foods before being replaced by Food Club and other Topco brands. This also includes Better Buy, Shurfine, Shursavings, and Marketchoice brands.

title: Associated Food Stores


text:
User talk:Craigdesson

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Hello, , and welcome to Wikipedia. Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers: I hope you enjoy editing here and being a Wikipedian! By the way, you can sign your name on Talk and vote pages using three tildes, like this: ~~~. Four tildes (~~~~) produces your name and the current date. If you have any questions, see the help pages, add a question to the village pump or ask me on my talk page. Again, welcome!}} -- Psy guy (talk) 20:34, 15 October 2005 (UTC)
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User talk:PatriciaMC

Welcome
Hello, , and welcome to Wikipedia. Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers: I hope you enjoy editing here and being a Wikipedian! By the way, you can sign your name on Talk and vote pages using three tildes, like this: ~~~. Four tildes (~~~~) produces your name and the current date. If you have any questions, see the help pages, add a question to the village pump or ask me on my talk page. Again, welcome!}} -- Psy guy (talk) 20:34, 15 October 2005 (UTC)
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title: User talk:PatriciaMC