Validation of the Eriksen Method of the Exact Foldy-Wouthuysen Representation

TL;DR

This paper confirms the validity of the Eriksen method for exact transformation to the Foldy-Wouthuysen representation, enabling better understanding of the applicability limits of approximate methods in relativistic quantum mechanics.

Contribution

It proves the Eriksen method's correctness and establishes criteria for when approximate step-by-step methods are valid.

Findings

Eriksen method yields exact FW transformation under certain conditions.

Comparison of relativistic Hamiltonians validates approximate methods.

Limits of applicability for step-by-step methods are clarified.

Abstract

The Eriksen method is proven to yield a correct and exact result when a sufficient condition of exact transformation to the Foldy-Wouthuysen (FW) representation is satisfied. Therefore, the Eriksen method is confirmed as valid. This makes it possible to establish the limits within which the approximate "step-by-step" methods are applicable. The latter is done by comparing the relativistic formulas for a Hamiltonian operator in the FW representation (obtained using those methods) and the known expression for the first terms of a series, which defines the expansion of this operator in powers of v/c as found by applying the Eriksen method.