The Gordon decompositions of the inertial currents of the Dirac electron correspond to a Foldy-Wouthuysen transformation
Ingo Kirsch, Lewis H. Ryder, Friedrich W. Hehl
Abstract
We consider Dirac's free electron theory on the first quantized level. We decompose its canonical spin current á 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.
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