Majorana spinor

The Majorana equation is a relativistic wave equation. It is named after the Italian physicist Ettore Majorana.

The Majorana equation is

with the derivative operator ${\displaystyle {\partial \!\!\!{\big /}}}$ written in Feynman slash notation to include the gamma matrices as well as a summation over the spinor components. In this equation ψ_c is the charge conjugate of ψ, which can be defined in the Majorana basis as

This relation leads to the alternate expression

In both cases, the quantity m is called the Majorana mass.

The Majorana is similar to the Dirac equation, but includes the charge conjugate ψ_c of a spinor ψ.

The appearance of both ψ and ψ_c in the Majorana equation means that the field ψ cannot be coupled to a charged electromagnetic field without violating charge conservation. To satisfy this restriction, ψ is taken to be neutral.

The quanta of the Majorana equation allow for two classes of particles, a neutral particle and its neutral antiparticle. The frequently applied supplemental condition ψ = ψ_c results in a single neutral particle, in which case ψ is known as a Majorana spinor. For a Majorana spinor, the Majorana equation is equivalent to the Dirac equation.

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