Connection Between Wave Functions in the Dirac and Foldy-Wouthuysen Representations

TL;DR

This paper establishes a precise relationship between wave functions in the Dirac and Foldy-Wouthuysen representations, showing conditions under which they differ only by constants and when lower spinors vanish.

Contribution

It derives an exact connection between wave functions in the Dirac and Foldy-Wouthuysen representations, clarifying their relationship under specific transformation conditions.

Findings

Upper spinors differ only by constant factors when transformation is exact

Lower spinors in Foldy-Wouthuysen representation are zero under exact transformation

Provides theoretical insight into the structure of wave functions in different representations

Abstract

The connection between wave functions in the Dirac and Foldy-Wouthuysen representations is found. When the Foldy-Wouthuysen transformation is exact, upper spinors in two representations differ only by constant factors, and lower spinors in the Foldy-Wouthuysen representation are equal to zero.