The Dirac equation vs. the Dirac type tensor equation

TL;DR

This paper explores the relationship between the traditional Dirac equation for electrons and a tensor-based Dirac type equation, highlighting their connection within the framework of ${ m U}(1)$ gauge symmetry.

Contribution

It introduces a novel perspective linking the Dirac equation to a tensor equation with gauge symmetry, expanding theoretical understanding.

Findings

Establishes a formal connection between Dirac and tensor equations.

Highlights the role of ${ m U}(1)$ gauge symmetry in both formulations.

Provides insights into potential unification of different quantum descriptions.

Abstract

We discuss a connection between the Dirac equation for an electron and the Dirac type tensor equation with ${\rm U}(1)$ gauge symmetry.