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a Generalized Quantum Electrodynamics.

Chihiro Kikuchi

Published Jan 1, 1944• 0 citations
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The Aharonov-Bohm (AB) effect is considered in the context of Generalized Electrodynamics (GE) by Podolsky and Bopp. GE is the only extension to Maxwell electrodynamics that is locally U(1)-gauge invariant, admits linear field equations and contains higher-order derivatives of the vector potential. GE admits both massless and massive modes for the photon. We recover the ordinary quantum phase shift of the AB effect, derived in the context of Maxwell electrodynamics, for the massless mode of the photon in GE. The massive mode induces a correction factor to the AB phase shift depending on the photon mass. We study both the magnetic AB effect and its electric counterpart. In principle, accurate experimental observations of AB the phase shift could be used to constrain GE photon mass.
Quantum electrodynamics under conditions of distinguishability of interacting matter entities, and of controlled actions and back-actions between them, is considered. Such ``mesoscopic quantum electrodynamics'' is shown to share its dynamical structure with the classical stochastic electrodynamics. In formal terms, we demonstrate that all general relations of the mesoscopic quantum electrodynamics may be recast in a form lacking Planck's constant. Mesoscopic quantum electrodynamics is therefore subject to ``doing quantum electrodynamics while thinking classically,'' allowing one to substitute essentially classical considerations for quantum ones without any loss in generality. Implications of these results for the quantum measurement theory are discussed.