Disformal invariance of Maxwell's field equations

TL;DR

This paper demonstrates that Maxwell's equations in vacuum are invariant under a new class of metric transformations called disformal mappings, extending conformal invariance and revealing a novel internal symmetry.

Contribution

It introduces and characterizes disformal invariance of Maxwell's equations, generalizing conformal invariance and exploring the associated group structure.

Findings

Maxwell's equations are invariant under disformal metric transformations.

Disformal mappings preserve gauge symmetry in electrodynamics.

The group structure of disformal transformations is analyzed in detail.

Abstract

We show that Maxwell's electrodynamics in vacuum is invariant under active transformations of the metric. These metrics are related by disformal mappings induced by derivatives of the gauge vector $A_{\mu}$ such that the gauge symmetry is preserved. Our results generalize the well known conformal invariance of electrodynamics and characterize a new type of internal symmetry of the theory. The group structure associated with these transformations is also investigated in details.