Aharonov-Bohm electrodynamics in material media: a scalar e.m. field cannot cause dissipation in a medium

TL;DR

This paper investigates an extended form of electromagnetism incorporating a scalar field and demonstrates that such scalar waves cannot propagate within material media, only reflecting or inducing gauge waves at the speed of light.

Contribution

It provides a theoretical analysis showing that scalar electromagnetic waves from the Aharonov-Bohm extension cannot propagate in dielectric or conducting media, only reflecting or generating gauge waves.

Findings

Scalar waves do not propagate in media.

Impinging scalar waves are reflected or generate gauge waves.

Gauge waves propagate at the speed of light with specific potential relations.

Abstract

In the extension of Maxwell equations based on the Aharonov-Bohm Lagrangian the e.m. field has an additional degree of freedom, namely a scalar field generated by charge and currents that are not locally conserved. We analyze the propagation of this scalar field through two different media (a pure dielectric and an ohmic conductor) in a range of frequencies such that the properties of the media are independent from the frequency. We find that an e.m. scalar wave cannot propagate in a material medium. If a scalar wave in vacuum impinges on a material medium it is reflected, at most exciting in the medium a pure "potential" wave (which we also call a "gauge" wave) propagating at $c$, the speed of light in vacuum, with a vector potential whose Fourier amplitude is related to that of the scalar potential by $\omega \mathbf{A}_{0}=\mathbf{k}\phi _{0}$, where $\omega^{2}=c^{2}\left\vert \mathbf{k}\right\vert^{2}$.