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,
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Costa de Beauregard, O. MPT versus: A manifestly covariant presentation of motion reversal and particle-antiparticle exchange. Found Phys 12, 861–871 (1982). https://doi.org/10.1007/BF01884997
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DOI: https://doi.org/10.1007/BF01884997