The Dirac equation for free particles

Textbook accounts of Dirac s free particle equation for the case s= 1/2 usually follow Dirac s original derivations [1] leading (in modem notation) to 

This is not in the Foldy canonical form (23), but can be transformed into it using the Foldy-Wouthuysen transformation [59] 

Equation (37) implies that H has energy eigenvalues (p) and that the position X in the Foldy representation leads to a velocity 

A key quantity in relativistic quantum theory is the charge-current density 

The proof that (x) transforms like a 4-vector with respect to Lorentz transfor- 

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