Galilean Covariance versus Gauge Invariance

TL;DR

This paper reveals that the Principle of Relativity determines gauge conditions in classical electromagnetism, linking them to physical continuity equations and highlighting a dual limit Galilean electromagnetism.

Contribution

It establishes a physical interpretation of gauge conditions as electromagnetic continuity equations and explores the implications for Galilean electromagnetism with dual limits.

Findings

Gauge conditions are physically interpreted as electromagnetic continuity equations.

Existence of a Galilean electromagnetism with electric and magnetic dual limits.

Phase-space domains depend on characteristic electromagnetic times.

Abstract

We demonstrate for the first time and unexpectedly that the Principle of Relativity dictates the choice of the "gauge conditions" in the canonical example of a Gauge Theory namely Classical Electromagnetism. All the known "gauge conditions" of the literature are interpreted physically as electromagnetic continuity equations hence the "gauge fields". The existence of a Galilean Electromagnetism with TWO dual limits ("electric" and "magnetic") is the crux of the problem [1]. A phase-space with the domains of validity of the various "gauge conditions" is provided and is shown to depend on three characteristic times : the magnetic diffusion time, the charge relaxation time and the transit time of electromagnetic waves in a continuous medium [2].