Dual gauge concepts in electrodynamics, and new limitations on gauge invariance

TL;DR

This paper explores dual interpretations of gauge invariance in electrodynamics, revealing fundamental differences and proposing new constraints on gauge transformations to unify the concept.

Contribution

It introduces a new limitation on gauge invariance that applies to both the Lagrangian symmetry-based and field-based gauge concepts.

Findings

Potential functions are more fundamental than fields.

Gauge transformations are constrained by physical symmetries.

A new universal gauge transformation limit is proposed.

Abstract

Gauge invariance, a core principle in electrodynamics, has two separate meanings. One concept treats the photon as the gauge particle for electrodynamics. It is based on symmetries of the Lagrangian, and requires no mention of electric or magnetic fields. The second concept depends directly on the electric and magnetic fields, and how they can be represented by potential functions that are not unique. A general proof that potentials are more fundamental than fields serves to resolve discrepancies. Physical symmetries, however, are altered by gauge transformations and strongly limit gauge freedom. A new constraint on the form of allowable gauge transformations must be introduced that applies to both gauge concepts.