Noether charges: the link between empirical significance of symmetries and non-separability

TL;DR

This paper explores how gauge symmetries can have direct empirical significance through the lens of Noether charges, linking gauge variance, non-locality, and non-separability in gauge theories.

Contribution

It establishes a connection between gauge-variance of charges, non-locality, and the empirical significance of symmetries, providing a new perspective on gauge invariance in bounded regions.

Findings

Gauge variance of charges relates to non-locality in gauge theories.

Non-separability is linked to the empirical significance of symmetries.

Local conservation laws imply conserved regional charges and non-separability.

Abstract

A fundamental tenet of gauge theory is that physical quantities should be gauge-invariant. This prompts the question: can gauge symmetries have physical significance? On one hand, the Noether theorems relate conserved charges to symmetries, endowing the latter with physical significance, though this significance is sometimes taken as indirect. But for theories in spatially finite and bounded regions, the standard Noether charges are not gauge-invariant. I here argue that gauge-\emph{variance} of charges is tied to the nature of the non-locality within gauge theories. I will flesh out these links by providing a chain of (local) implications: `local conservation laws'${\Rightarrow}$ `conserved regional charges' $\Leftrightarrow$ `non-separability' ${\Leftrightarrow}$ `direct empirical significance of symmetries'.