Majorana equation

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 in the sense that it involves four-component spinors, gamma matrices and mass terms, but includes the charge conjugate ψ_c of a spinor ψ. In contrast, the Weyl equation is for two-component spinor without mass.

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, since particles have the opposite charge to their own antiparticles. To satisfy this restriction, ψ must be taken to be neutral.

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