Classical Limit of Relativistic Quantum Mechanical Equations in the Foldy-Wouthuysen Representation

TL;DR

This paper demonstrates that under WKB approximation, the Foldy-Wouthuysen representation simplifies deriving the classical limit of relativistic quantum equations by replacing operators with classical variables.

Contribution

It shows that the Foldy-Wouthuysen representation enables a straightforward operator-to-classical variable transition under WKB conditions.

Findings

Classical limit derivation is simplified using the Foldy-Wouthuysen representation.

Operators in the Hamiltonian are replaced by classical quantities under WKB approximation.

The approach clarifies the connection between relativistic quantum mechanics and classical physics.

Abstract

It is shown that, under the Wentzel-Kramers-Brillouin approximation conditions, using the Foldy-Wouthuysen representation allows the problem of finding a classical limit of relativistic quantum mechanical equations to be reduced to the replacement of operators in the Hamiltonian and quantum mechanical equations of motion by the respective classical quantities.