Gauge transformations and symmetry violations

Howard R. Reiss

Published Dec 6, 2017• 1 citation

Abstract

A nominally legitimate set of electromagnetic potentials to represent electric and magnetic fields can cause violation of basic symmetries in both classical and quantum applications, creating errors in dynamical calculations. Preservation of symmetries places constraints on the choice of potentials and thus constitutes a robust reason to regard electromagnetic potentials as more fundamental than electromagnetic fields. This represents a major extension of the quantum-only example of the Aharonov-Bohm effect for establishing the primacy of potentials over fields. Symmetry violation caused by inappropriate gauge choice means that gauge transformations are not necessarily unitary, since they do not ensure preservation of the values of physical observables. Unitarity is examined in the Schr\odinger equation and in transition amplitudes.

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