Noether charges: the link between empirical significance of symmetries 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'.