Operators of Dirac's theory with mass and axial chemical potential

TL;DR

This paper analytically solves the Dirac equation with mass and axial chemical potential, defining new spin operators and quantization methods for massive fermions in free and axial potential environments.

Contribution

It introduces the first definition of the odd partner of Pryce spin operator and develops a framework for particle-antiparticle spin and polarization operators in Dirac's theory.

Findings

Analytical solutions for Dirac equation with axial chemical potential.

New definitions of spin and polarization operators for fermions.

Distinct operator algebras for free and axial potential cases.

Abstract

The Dirac equation with mass and axial chemical potential is solved analytically obtaining the mode spinors and corresponding projection operators giving the spectral representations of the principal conserved operators. In this framework, the odd partner of the Pryce spin operator is defined for the first time showing how these operators may be combined for defining the particle and antiparticle spin and polarization operators of Dirac's theory of massive fermions either in the free case or in the presence of the axial chemical potential. The quantization procedure is applied in both these cases obtaining two distinct operator algebras in which the particle and antiparticle spin and polarization operators take canonical forms. In this approach statistical operators with independent particle and antiparticle vortical chemical potentials may be constructed.