Foundations of Physics

, Volume 19, Issue 10, pp 1125–1149 | Cite as

Off-shell electromagnetism in manifestly covariant relativistic quantum mechanics

  • David Saad
  • L. P. Horwitz
  • R. I. Arshansky


Gauge invariance of a manifestly covariant relativistic quantum theory with evolution according to an invariant time τ implies the existence of five gauge compensation fields, which we shall call pre-Maxwell fields. A Lagrangian which generates the equations of motion for the matter field (coinciding with the Schrödinger type quantum evolution equation) as well as equations, on a five-dimensional manifold, for the gauge fields, is written. It is shown that τ integration of the equations for the pre-Maxwell fields results in the usual Maxwell equations with conserved current source. The analog of the O (3, 1) symmetry of the usual Maxwell theory is found to be O (3, 2) or O (4, 1), depending on the space-time Fourier spectrum of the field. We argue that the structure that is relevant to the description of radiation in interaction with matter evolving in a timelike sense is that of O (3, 2). The noncovariant form of the field equations is given; there are two fields of electric type and one (divergenceless) magnetic type field. The Noether currents are studied, and some remarks are made on second quantization.


Manifold Gauge Invariance Fourier Spectrum Gauge Field Matter Field 
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Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • David Saad
    • 1
  • L. P. Horwitz
    • 2
  • R. I. Arshansky
    • 2
  1. 1.Department of Electromagnetic Devices and Radiation, Faculty of EngineeringTel Aviv UniversityRamat AvivIsrael
  2. 2.School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityRamat AvivIsrael

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