Majorana equation

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The Majorana equation is a relativistic wave equation similar to the Dirac equation but includes the charge conjugate ψ_c of a spinor ψ. It is named after the Italian Ettore Majorana, and it is

$i \hbar {\partial\!\!\!\big /} \psi - m c \psi_c = 0 \qquad \qquad (1)$

written in Feynman notation, where the charge conjugate is defined as

$\psi_c := \gamma^2 \psi^*\$ .

Equation (1) can alternatively be expressed as

$i\hbar {\partial\!\!\!\big /} \psi_c - mc \psi = 0 \qquad \qquad (2)$ .

If a particle has a spinor wavefunction ψ which satisfies the Majorana equation, then the quantity m in the equation is called the Majorana mass. If ψ = ψ_c then ψ is called a Majorana spinor. Unlike Weyl spinors or Dirac spinors, the Majorana spinor is a real representation of the Lorentz group, which is why we are permitted to include both the spinor and its "complex conjugate" in the same equation. Actually, there is another way^[clarify] of writing a Majorana spinor in terms of four real components, which shows why the "complex conjugation" is sometimes referred to as an artifact of using the Dirac notation for a real spinor.