Exact form of the exponential Foldy-Wouthuysen transformation operator for an arbitrary-spin particle

TL;DR

This paper derives an exact exponential Foldy-Wouthuysen transformation operator for particles of any spin, providing a tool to verify and derive Hamiltonians in relativistic quantum mechanics.

Contribution

It presents the first exact exponential operator for the Foldy-Wouthuysen transformation applicable to arbitrary-spin particles, enabling validation of existing methods.

Findings

Provides an exact exponential operator for arbitrary-spin particles.

Facilitates verification of Foldy-Wouthuysen transformation methods.

Enables derivation of Hamiltonians for relativistic particles.

Abstract

The exact exponential Foldy-Wouthuysen transformation operator applicable for a particle with an arbitrary spin is derived. It can be successfully utilized for verifying any Foldy-Wouthuysen transformation method based on the exponential operator. When a verified method is relativistic, the relativistic exponential operator should be expanded in the semirelativistic power series. The use of the obtained exponential operator for a derivation of the Foldy-Wouthuysen Hamiltonian makes it possible to check the validity of any other method of the Foldy-Wouthuysen transformation, while this possibility may need a greater computational effort.