Foldy-Wouthuysen Transformation and Semiclassical Transition for Relativistic Quantum Mechanics

TL;DR

This paper demonstrates that the Foldy-Wouthuysen transformation enables a consistent classical limit of relativistic quantum mechanics, showing full agreement between quantum and classical descriptions for particles with any spin.

Contribution

It establishes the semiclassical equations of motion and spin dynamics as identical to classical equations, extending the Bohr correspondence principle to all spins and spinless particles.

Findings

Quantum and classical equations coincide for relativistic particles.

Semiclassical spin dynamics match classical spin equations.

Bohr's correspondence principle applies broadly to particles of any spin.

Abstract

It is shown that the Foldy-Wouthuysen transformation for relativistic particles in strong external fields provides the possibility of obtaining a meaningful classical limit of the relativistic quantum mechanics. The full agreement between quantum and classical theories is proved. The coincidence of the semiclassical equations of motion of particles and their spins with the corresponding classical equations is established. The Niels Bohr's correspondence principle is valid not only in the limit of large spin quantum numbers but also for particles with any spin as well as for spinless particles.