The Gordon decompositions of the inertial currents of the Dirac electron correspond to a Foldy-Wouthuysen transformation

TL;DR

This paper demonstrates that the Gordon decomposition of the Dirac electron's inertial currents is equivalent to a Foldy-Wouthuysen transformation, linking different representations of the Dirac wave function.

Contribution

It establishes a direct connection between the Gordon decomposition and the Foldy-Wouthuysen transformation in Dirac theory, clarifying their equivalence.

Findings

Gordon spin current is conserved and equivalent to Hilgevoord-Wouthuysen spin.

Gordon decomposition corresponds to a Foldy-Wouthuysen transformation.

Transforms Dirac wave function between Dirac-Pauli and Newton-Wigner representations.

Abstract

We consider Dirac's free electron theory on the first quantized level. We decompose its canonical spin current \'a la Gordon and find a conserved ``Gordon spin'' current which turns out to be equivalent to the Hilgevoord-Wouthuysen spin. We can conclude therefrom that the Gordon-type decomposition mentioned above corresponds to a Foldy-Wouthuysen transformation which transforms the Dirac wave function from the conventional Dirac-Pauli to the Newton-Wigner representation.