Exact Foldy-Wouthuysen transformation for a Dirac equation describing the interaction of spin-1/2 relativistic particles with an external electromagnetic field

TL;DR

This paper derives the Thomas-Bargmann-Michel-Telegdi equation using an exact Foldy-Wouthuysen transformation, revealing new terms and providing a detailed procedure for obtaining the general result in relativistic quantum mechanics.

Contribution

It presents a detailed method for applying the Exact Foldy-Wouthuysen transformation to Dirac particles in electromagnetic fields, including new terms and insights into parametrization choices.

Findings

Derived the T-BMT equation via exact FW transformation.

Identified new terms in the transformed equations.

Provided a systematic procedure for the transformation.

Abstract

The Thomas-Bargmann-Michel-Telegdi (T-BMT) equation is derived using the Exact Foldy-Wouthuysen transformation. Extra new terms were found, and we discuss their possible physical applications. The main point of this work is to detail the procedure to get the general result. We explicitly present the choice of parametrization we used on the initial Hamiltonian and the motivations to take it. We emphasize that the final equations can depend on this choice, and it is possible to prevent the manipulations of the quadratic Hamiltonian become extremely cumbersome. More importantly, it is done in such a way that the transformed equations allow the direct separation into mass, kinetic, and interaction correction terms to the original T-BMT equation.