Temporal vs Spatial Conservation and Memory Effect in Electrodynamics

TL;DR

This paper explores the interplay between temporal and spatial conservation laws and memory effects in Maxwell's electrodynamics with boundaries, revealing new insights into gauge symmetries and associated charges.

Contribution

It introduces the concept of spatial memory fields and demonstrates their relation to conservation laws, extending the understanding of gauge symmetries in bounded electrodynamics.

Findings

Charge conservation is linked to gauge symmetry at boundaries.

Spatial memory effects are formally defined and related to conservation laws.

The connection between spatial memory and conservation mirrors temporal cases in gauge theories.

Abstract

We consider the standard Maxwell's theory in 1+3 dimensions in the presence of a timelike boundary. In this context, we show that (generalized) Ampere-Maxwell's charge appears as a Noether charge associated with the Maxwell U(1) gauge symmetry which satisfies a spatial conservation equation. Furthermore, we also introduce the notion of spatial memory field and its corresponding memory effect. Finally, similar to the temporal case through the lens of Strominger's triangle proposal, we show how spatial memory and conservation are related.