Generalization of exact operators of the Foldy-Wouthuysen transformation to arbitrary-spin particles in nonstationary fields

TL;DR

This paper extends the Foldy-Wouthuysen transformation to arbitrary-spin particles in nonstationary fields, providing exact operators and analyzing their properties for a better quantum-mechanical description.

Contribution

It generalizes the exact operators of the Foldy-Wouthuysen transformation to particles with any spin in time-dependent fields, including fundamental properties.

Findings

Derived exact nonexponential and exponential operators for arbitrary spins.

Identified fundamental properties of these operators and the Hamiltonian.

Enhanced the quantum description of particles in nonstationary fields.

Abstract

Time-dependent terms in Hamiltonians and equations of motion are rather important for a quantum-mechanical description of particles with arbitrary spins in nonstationary fields. We use the Foldy-Wouthuysen representation which allows one to obtain the Schr\"{o}dinger picture of relativistic quantum mechanics. We determine exact nonexponential and exponential operators of the Foldy-Wouthuysen transformation for arbitrary-spins particles in the nonstationary case. Some fundamental properties of these operators and the Foldy-Wouthuysen Hamiltonian are also identified.