Gauge Is More Than Mathematical Redundancy

TL;DR

This paper explores how gauge invariance reflects the relational nature of physical degrees of freedom, clarifying recent boundary variable developments by emphasizing the informational differences when splitting gauge systems.

Contribution

It reveals that gauge invariance formalizes the relational aspect of physical degrees of freedom and explains the informational loss when dividing gauge systems into subsystems.

Findings

Gauge-invariant variables of subsystems contain less information than those of the whole system.

Boundary variables and charges are clarified through the relational perspective.

Gauge invariance encodes the relational nature of physical degrees of freedom.

Abstract

Physical systems may couple to other systems through variables that are not gauge invariant. When we split a gauge system into two subsystems, the gauge-invariant variables of the two subsystems have less information than the gauge invariant variables of the original system; the missing information regards degrees of freedom that express relations between the subsystems. All this shows that gauge invariance is a formalization of the relational nature of physical degrees of freedom. The recent developments on boundary variables and boundary charges are clarified by this observation.