On the non-uniqueness problem of the covariant Dirac theory and the spin-rotation coupling

TL;DR

This paper investigates the non-uniqueness of the covariant Dirac theory's Hamiltonian formulations, demonstrating that different Hamiltonians can be physically non-equivalent, thus emphasizing the need for experimental verification of the spin-rotation coupling.

Contribution

It critically examines claims of uniqueness in the covariant Dirac theory and shows that the spin-rotation coupling term's physical reality remains unconfirmed.

Findings

Two Hamiltonians in the same frame are non-equivalent

The spin-rotation coupling term's reality is unverified

Claims of a unique prescription are challenged

Abstract

Gorbatenko & Neznamov [arXiv:1301.7599] recently claimed the absence of the title problem. In this paper, the reason for that problem is reexplained by using the notions of a unitary transformation and of the mean value of an operator, invoked by them. Their arguments actually aim at proving the uniqueness of a particular prescription for solving this problem. But that prescription is again shown non-unique. Two Hamiltonians in the same reference frame in a Minkowski spacetime, only one of them including the spin-rotation coupling term, are proved to be physically non-equivalent. This confirms that the reality of that coupling should be checked experimentally.