General method of the relativistic Foldy-Wouthuysen transformation and proof of validity of the Foldy-Wouthuysen Hamiltonian

TL;DR

This paper introduces a comprehensive and rigorous method for the relativistic Foldy-Wouthuysen transformation applicable to particles of any spin in strong external fields, confirming the validity of the derived Hamiltonian.

Contribution

A new general method for the relativistic Foldy-Wouthuysen transformation that satisfies the exact transformation condition and applies to particles with any spin in strong fields.

Findings

The method is applicable to relativistic particles with any spin.

The derived Hamiltonian matches previous iterative results.

The approach is well substantiated and exact under specified conditions.

Abstract

A general method of the Foldy-Wouthuysen transformation is developed. This method is applicable to relativistic particles with any spin in arbitrarily strong external fields. It can be used when the de Broglie wavelength is much smaller than the characteristic distance. Contrary to previously developed relativistic methods, the present method satisfies the condition of the exact Foldy-Wouthuysen transformation and is well substantiated. The derived relativistic Foldy-Wouthuysen Hamiltonian is expanded in powers of the Planck constant. In this expansion, terms proportional to the zero and first powers are determined exactly in accordance with the above condition and terms proportional to higher powers are not specified. The obtained result agrees with the corresponding formula for the Foldy-Wouthuysen Hamiltonian previously deduced by an iterative relativistic method and proves the validity of results obtained with this formula.