Summary of a non-uniqueness problem of the covariant Dirac theory and of two solutions of it

TL;DR

This paper discusses the non-uniqueness issue of the covariant Dirac theory's Hamiltonian and energy operators, explores two methods to resolve it, and examines their implications in a rotating reference frame, revealing a spin-rotation coupling only in one method.

Contribution

It introduces two approaches to fix the gauge freedom in the covariant Dirac theory and analyzes their effects in a rotating frame, highlighting differences in physical predictions.

Findings

Non-uniqueness of Hamiltonian and energy operators in covariant Dirac theory.

Two methods to restrict gauge freedom to resolve the non-uniqueness.

Spin-rotation coupling appears only with one of the proposed methods.

Abstract

We present a summary of: 1) the non-uniqueness problem of the Hamiltonian and energy operators associated, in any given coordinate system, with the generally-covariant Dirac equation; 2) two different ways to restrict the gauge freedom so as to solve that problem; 3) the application of these two ways to the case of a uniformly rotating reference frame in Minkowski spacetime: we find that a spin-rotation coupling term is there only with one of these two ways.