Multipole charge conservation and implications on electromagnetic radiation

TL;DR

This paper reveals that certain residual gauge symmetries in Maxwell's theory correspond to conserved multipole charges, linking source moments and electromagnetic fields, and constraining radiation through these conserved quantities.

Contribution

It introduces the concept of multipole charges as residual gauge symmetries, connecting electric multipole moments with conserved charges and their role in electromagnetic radiation.

Findings

Multipole charges are proportional to electric multipole moments.

These charges receive contributions from both sources and fields.

Conservation of multipole charges constrains electromagnetic radiation.

Abstract

It is shown that conserved charges associated with a specific subclass of gauge symmetries of Maxwell electrodynamics are proportional to the well known electric multipole moments. The symmetries are residual gauge transformations surviving after fixing the Lorenz gauge, and have nontrivial charge. These "Multipole charges" receive contributions both from the charged matter and electromagnetic fields. The former is nothing but the electric multipole moment of the source. In a stationary configuration, there is a novel equipartition relation between the two contributions. The multipole charge, while conserved, can freely interpolate between the source and the electromagnetic field, and therefore can be propagated with the radiation. Using the multipole charge conservation, we obtain infinite number of constraints over the radiation produced by the dynamics of charged matter.