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arXiv · 1311.5423

Double gauge invariance and covariantly-constant vector fields in Weyl geometry

Vladimir V. Kassandrov·Joseph A. Rizcallah
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Abstract

The wave equation and equations of covariantly-constant vector fields (CCVF) in spaces with Weyl nonmetricity turn out to possess, in addition to the canonical conformal-gauge, a gauge invariance of another type. On a Minkowski metric background, the CCVF system alone allows us to pin down the Weyl 4-metricity vector, identified herein with the electromagnetic potential. The fundamental solution is given by the ordinary Lienard-Wiechert field, in particular, by the Coulomb distribution for a charge at rest. Unlike the latter, however, the magnitude of charge is necessarily unity, "elementary", and charges of opposite signs correspond to retarded and advanced potentials respectively, thus establishing a direct connection between the particle/antiparticle asymmetry and the "arrow of time".

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Vladimir V. Kassandrov, Joseph A. Rizcallah. 2013-11-20. Double gauge invariance and covariantly-constant vector fields in Weyl geometry. https://doi.org/10.1007/s10714-014-1772-5

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