Discrete Symmetries of Off-Shell Electromagnetism
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This paper discusses the discrete symmetries of off-shell electromagnetism, the Stueckelberg–Schrodinger relativistic quantum theory and its associated 5D local gauge theory. Seeking a dynamical description of particle/antiparticle interactions, Stueckelberg developed a covariant mechanics with a monotonically increasing Poincaré-invariant parameter. In Stueckelberg’s framework, worldlines are traced out through the parameterized evolution of spacetime events, which may advance or retreat with respect to the laboratory clock, depending on the sign of the energy, so that negative energy trajectories appear 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.
Key wordscharge conjugation parity time reversal
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- E. C. G. Stueckelberg, it Helv. Phys. Acta bf 14, 322 (1941),newline E. C. G. Stueckelberg, it Helv. Phys. Acta bf 14, 588 (1941).Google Scholar
- Eugene P. Wigner, Group Theory and its Application to the Quantum Mechanics of Atomic Spectra (Academic, New York, 1959); E. Wigner, it Nachr. Akad. Ges. Wiss. G"ottingen bf 31, 546 (1932).Google Scholar
- Itzykson, C., Zuber, J.-B. 1980Quantum Field TheoryMcGraw-HillNew YorkGoogle Scholar
- Horwitz, L.P., Piron, C. 1973Helv. Phys. Acta.48316Google Scholar
- L. P. Horwitz and Y. Lavie, it Phys. Rev. D bf 26, 819 (1982) R. I. Arshansky and L. P. Horwitz, it J. Math. Phys. bf 30, 213 (1989); R. I. Arshansky and L. P. Horwitz, it Phys. Lett A bf 131, 222 (1988).Google Scholar
- M. C. Land, N. Shnerb, and L. P. Horwitz, it J. Math. Phys. bf 36, 3263 (1995), F. J. Dyson, it Am. J. Phys. bf 58, 209 (1990); Shogo Tanimura, it Ann. Phys. bf 220, 229 (1992).Google Scholar
- Land M., C. 1996Found. Phys.2719Google Scholar
- Yu, , Novozhilov, V. 1975Introduction to Elementary Particle TheoryPergamonOxfordGoogle Scholar
- Jackson J., D. 1975Classical ElectrodynamicsWileyNew YorkGoogle Scholar