Free Form of the Foldy-Wouthuysen Transformation in External Electromagnetic Fields

TL;DR

This paper derives an exact, free-form Foldy-Wouthuysen transformation for Dirac fermions in static electromagnetic fields using Ritus eigenfunctions, simplifying the analysis of relativistic quantum particles in external fields.

Contribution

It introduces a novel exact transformation framework for Dirac fermions in static electromagnetic fields based on Ritus eigenfunctions, enabling simplified calculations.

Findings

Exact FW transformation derived in Ritus basis.

Transformation involves dynamical quantum numbers.

Facilitates analysis of Dirac particles in external fields.

Abstract

We derive the exact Foldy-Wouthuysen transformation for Dirac fermions in a time independent external electromagnetic field in the basis of the Ritus eigenfunctions, namely the eigenfunctions of the operator $(\gamma \cdot \Pi)^2$, with $\Pi^\mu = p^\mu - e A^\mu$. In this basis, the transformation acquires a free form involving the dynamical quantum numbers induced by the field.