# On the calculation of covariant expressions for Dirac bilinears

## TL;DR

This paper reviews methods for calculating covariant Dirac bilinears, presenting algebraic and tensorial approaches that express these bilinears in terms of Lorentz scalars for use in relativistic quantum theories.

## Contribution

It introduces a covariant framework for expressing Dirac bilinears entirely in terms of Lorentz scalars, simplifying calculations in relativistic quantum field theory.

## Key findings

- Provides algebraic equations for Dirac spinors.
- Develops a covariant spacetime parameterization approach.
- Offers a recipe for scalar bilinear calculations.

## Abstract

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.