On the calculation of covariant expressions for Dirac bilinears

In this article, various approaches to calculate covariant expressions for the bilinears of Dirac spinors are presented. For this purpose, algebraic equations defining Dirac spinors are discussed. Following that, a covariant approach for spacetime parameterization is presented and the equations defining Dirac spinors are written fully in terms of Lorentz scalars. After presenting how the tensorial bilinears can be reduced to combinations of scalar bilinears with appropriate Lorentz structures, a covariant recipe for the calculation of scalar bilinears is provided.

Automated summary

This article presents various approaches to calculate covariant expressions for the bilinears of Dirac spinors, discussing the algebraic equations defining Dirac spinors and providing a covariant approach for spacetime parameterization. It also shows how tensorial bilinears can be reduced to combinations of scalar bilinears with appropriate Lorentz structures, and offers a covariant recipe for the calculation of scalar bilinears.