Discrete Symmetries of Off-Shell Electromagnetism

TL;DR

This paper explores the discrete symmetries of off-shell electromagnetism within a 5D gauge theory framework, revealing how charge conjugation and CPT symmetries manifest in both classical and quantum contexts with Lorentz covariance.

Contribution

It introduces a 5D local gauge theory for off-shell electromagnetism that exhibits tensorial transformation properties under discrete symmetries, unifying classical and quantum charge conjugation.

Findings

Gauge fields transform tensorially under reflections.

Charge conjugation involves simultaneous reflection of evolution sense and scalar field.

Classical interactions do not distinguish particles from antiparticles.

Abstract

We discuss the discrete symmetries of the Stueckelberg-Schrodinger relativistic quantum theory and its associated 5D local gauge theory, a dynamical description of particle/antiparticle interactions, with monotonically increasing Poincare-invariant parameter. In this framework, worldlines are traced out through the parameterized evolution of spacetime events, advancing or retreating with respect to the laboratory clock, with negative energy trajectories appearing as antiparticles when the observer describes the evolution using the laboratory clock. The associated gauge theory describes local interactions between events (correlated by the invariant parameter) mediated by five off-shell gauge fields. These gauge fields are shown to transform tensorially under under space and time reflections, unlike the standard Maxwell fields, and the interacting quantum theory therefore remains manifestly Lorentz covariant. Charge conjugation symmetry in the quantum theory is achieved by simultaneous reflection of the sense of evolution and the fifth scalar field. Applying this procedure to the classical gauge theory leads to a purely classical manifestation of charge conjugation, placing the CPT symmetries on the same footing in the classical and quantum domains. In the resulting picture, interactions do not distinguish between particle and antiparticle trajectories -- charge conjugation merely describes the interpretation of observed negative energy trajectories according to the laboratory clock.