On the mass term of the Dirac equation

TL;DR

This paper generalizes the Dirac equation by allowing the mass term to be an arbitrary matrix, deriving its general form, and proving its equivalence to the standard Dirac equation.

Contribution

It introduces a generalized mass matrix form in the Dirac equation and demonstrates its equivalence to the original formulation.

Findings

Derived the general form of the mass matrix M.

Proved the equivalence of the generalized and original Dirac equations.

Abstract

We consider the generalization of the Dirac equation where the mass term is an arbitrary matrix M. A general form of M, consistent with the mass shell constraint, is derived and proven to be equivalent to the original Dirac equation.