Particles and events in classical off-shell electrodynamics |
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Authors: | M C Land |
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Institution: | (1) Department of Communications Engineering, The Center for Technological Education Holon Affiliated with Tel Aviv University, P.O. Box 305, 58102 Holon, Israel |
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Abstract: | Despite the many successes of the relativistic quantum theory developed by Horwitz et al., certain difficulties persist in
the associated covariant classical mechanics. In this paper, we explore these difficulties through an examination of the classical.
Coulomb problem in the framework of off-shell electrodynamics. As the local gauge theory of a covariant quantum mechanics
with evolution paratmeter τ, off-shell electrodynamics constitutes a dynamical theory of ppacetime events, interacting through
five τ-dependent pre-Maxwell potentials. We present a straightforward solution of the classical equations of motion, for a
test event traversing the field induced by a “fixed” event (an event moving uniformly along the time axis at a fixed point
in space). This solution is seen to be unsatisfactory, and reveals the essential difficulties in the formalism at the classical
levels. We then offer a new model of the particle current—as a certain distribution of the event currents on the worldline—which
eliminates these difficulties and permits comparison of classisical off-shell electrodynamics with the standard Maxwell theory.
In this model, the “fixed” event induces a Yukawa-type potential, permitting a semiclassical identification of the pre-Maxwell
time scale λ with the inverse mass of the intervening photon. Numerical solutions to the equations of motion are compared
with the standard Maxwell solutions, and are seen to coincide when λ≳10−6 seconds, providing an initial estimate of this parameter. It is also demonstrated that the proposed model provides a natural
interpretation for the photon mass cut-off required for the renormalizability of the off-shell quantum electrodynamics. |
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