Splitting the Dirac equation: the case of longitudinal potentials

TL;DR

This paper demonstrates that the Dirac equation with longitudinal external potentials can be decomposed into two covariant subequations, extending previous work on free equations to interacting cases.

Contribution

It introduces a method to split the Dirac equation with longitudinal potentials into covariant subequations, revealing new structural insights.

Findings

Dirac equation in longitudinal fields can be split into two covariant subequations

Extension of previous free equation results to interacting cases

Provides a framework for analyzing Dirac equations with external potentials

Abstract

Recently, we have demonstrated that some subsolutions of the free Duffin-Kemmer-Petiau and the Dirac equations obey the same Dirac equation with some built-in projection operators. In the present paper we study the Dirac equation in the interacting case. It is demonstrated that the Dirac equation in longitudinal external fields can be also splitted into two covariant subequations.