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

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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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Acknowledgments

We would like to thank Profs. D.V. Alexeevski, A.Ya. Burinskii, B. N. Frolov and A. S. Rabinowitch for friendly discussions and valuable comments. The authors are also indebted to the referees for critical remarks and advices which helped to improve the paper and stimulated subsequent work. One of the authors (V. K.) wants to express his particular gratitude to Prof. E.T. Newman for the long-term support and kind attention.

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Authors and Affiliations

  1. Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia, Moscow, Russia

    Vladimir V. Kassandrov

  2. School of Education, Lebanese University, Beirut, Lebanon

    Joseph A. Rizcallah

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  1. Vladimir V. Kassandrov
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  2. Joseph A. Rizcallah
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Correspondence to Vladimir V. Kassandrov.

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Kassandrov, V.V., Rizcallah, J.A. Double gauge invariance and covariantly-constant vector fields in Weyl geometry. Gen Relativ Gravit 46, 1772 (2014). https://doi.org/10.1007/s10714-014-1772-5

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