MPT versus: A manifestly covariant presentation of motion reversal and particle-antiparticle exchange

Abstract

We show that particle-antiparticle exchange and covariant motion reversal are two physically different aspects of the same mathematical transformation, either in the prequantal relativistic equation of motion of a charged point particle, in the general scheme of second quantization, or in the spinning wave equations of Dirac and of Petiau-Duffin-Kemmer. While, classically, charge reversal and rest mass reversal are equivalent operations, in the wave mechanical case mass reversal must be supplemented by exchange of the two adjoint equations, implying ψ ⇄$\bar \psi$.

Denoting by M the rest mass reversal, P the parity reversal, T the Racah time reversal, and Z the ψ ⇄$\bar \psi$ exchange, the connection with the usual

scheme of charge conjugation, parity reversal, and Wigner motion reversal, is

with, of course,