Lorentz invariance violation and charge (non--)conservation: A general theoretical frame for extensions of the Maxwell equations

TL;DR

This paper develops a comprehensive theoretical framework extending Maxwell's equations to include Lorentz invariance violation and charge non-conservation, linking these to various quantum gravity models and proposing experimental tests.

Contribution

It introduces a more general phenomenological approach than the SME, encompassing charge non-conservation and suggesting new experimental avenues.

Findings

Extended Maxwell equations cover Lorentz violation and charge non-conservation.

CNC linked to polarization precession and Coulomb potential modifications.

No definitive experimental tests of charge conservation currently exist.

Abstract

All quantum gravity approaches lead to small modifications in the standard laws of physics which lead to violations of Lorentz invariance. One particular example is the extended standard model (SME). Here, a general phenomenological approach for extensions of the Maxwell equations is presented which turns out to be more general than the SME and which covers charge non--conservation (CNC), too. The new Lorentz invariance violating terms cannot be probed by optical experiments but need, instead, the exploration of the electromagnetic field created by a point charge or a magnetic dipole. Some scalar--tensor theories and higher dimensional brane theories predict CNC in four dimensions and some models violating Special Relativity have been shown to be connected with CNC and its relation to the Einstein Equivalence Principle has been discussed. Due to this upcoming interest, the experimental status of electric charge conservation is reviewed. Up to now there seem to exist no unique tests of charge conservation. CNC is related to the precession of polarization, to a modification of the $1/r$--Coulomb potential, and to a time-dependence of the fine structure constant. This gives the opportunity to describe a dedicated search for CNC.