# New explicit expressions for Dirac bilinears

## TL;DR

This paper derives new explicit formulas for Dirac bilinears that depend on a Minkowski space direction, valid for all momenta and polarizations, highlighting the role of Wigner rotations in relativistic spin theory.

## Contribution

It introduces a novel, general expression for Dirac bilinears incorporating a Minkowski space direction, extending applicability beyond previous formulas.

## Key findings

- New explicit Dirac bilinear expressions valid for all momenta
- Dependence on Minkowski space direction due to Wigner rotations
- Generic explicit expression for covariant spin vector

## Abstract

We derive new explicit expressions for the Dirac bilinears based on a generic representation of the massive Dirac spinors with canonical polarization. These bilinears depend on a direction $n$ in Minkowski space which specifies the form of dynamics. We argue that such a dependence is unavoidable in a relativistic theory with spin, since it originates from Wigner rotation effects. Contrary to most of the expressions found in the literature, our ones are valid for all momenta and canonical polarizations of the spinors. As a by-product, we also obtain a generic explicit expression for the covariant spin vector.