Validation of the Eriksen method for the exact Foldy-Wouthuysen representation

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 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.