Abstract
The dynamical equations of relativistic quantum mechanics prescribe the motion of wave packets for sets of events which trace out the world lines of the interacting particles. Electromagnetic theory suggests thatparticle world line densities be constructed from concatenation of event wave packets. These sequences are realized in terms of conserved probability currents. We show that these conserved currents provide a consistent particle and antiparticle interpretation for the asymptotic states in scattering processes. The relation between current conservation and unitarity is used to establish relations between pair production and annihilation amplitudes and scattering. The discrete symmetriesC, T, P are studied and it is shown that no Dirac sea (for fermions where such a construction is possible, or bosons where it is not) is required for consistency of the theory. These currents, furthermore, represent the discrete symmetries in a way consistent with their interpretation as particle currents.
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This work was supported in part by the Binational Science Foundation (BSF), Jerusalem, Israel. A preliminary report was given at the Conference on Statistical Mechanics and Irreversible Processes, San Antonio, Texas, March 14–17, 1982.
The first two authors dedicate this paper to the memory of their friend and colleague, Yeshiahu (Ishi) Lavie, who died in the service of the Israel Defense Forces, January 2, 1983.
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Arshansky, R., Horwitz, L.P. & Lavie, Y. Particles vs. events: The concatenated structure of world lines in relativistic quantum mechanics. Found Phys 13, 1167–1194 (1983). https://doi.org/10.1007/BF00727992
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DOI: https://doi.org/10.1007/BF00727992