Strong limitations on allowable gauge transformations in electrodynamics

TL;DR

This paper argues that conservation principles in electrodynamics impose strict limitations on gauge transformations, emphasizing the fundamental role of potentials over fields and highlighting the radiation gauge as the practical choice when transverse and longitudinal fields coexist.

Contribution

It demonstrates that conservation laws restrict gauge transformations in electrodynamics, establishing the primacy of potentials and identifying the radiation gauge as the only practical gauge under certain conditions.

Findings

Potentials are essential for conservation principles in electrodynamics.

Gauge transformations are severely limited by conservation conditions.

Radiation gauge is the only practical gauge when transverse and longitudinal fields coexist.

Abstract

Conservation principles establish the primacy of potentials over fields in electrodynamics, both classical and quantum. The contrary conclusion that fields are primary is based on the Newtonian concept that forces completely determine dynamics, and electromagnetic forces depend directly on fields. However, physical conservation principles come from symmetries such as those following from Noether's theorem, and these require potentials for their statement. Examples are given of potentials that describe fields correctly but that violate conservation principles, demonstrating that the correct statement of potentials is necessary. An important consequence is that gauge transformations are severely limited when conservation conditions must be satisfied. When transverse and longitudinal fields are present concurrently, the only practical gauge is the radiation gauge.