Gauge Is More Than Mathematical Redundancy

Understand

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.