Gauging the Boundary in Field-space

Understand

Local gauge theories are in a complicated relationship with boundaries.

• Whereas fixing the gauge can often shave off unwanted redundancies, the coupling of different bounded regions requires the use of gauge-variant elements.
• Therefore, coupling is inimical to gauge-fixing, as usually understood.
• This sort of reasoning has led some to declare the coupling of subsystems to be the raison d'\^etre of gauge.