Spacetime boundaries do not break diffeomorphism and gauge symmetries

In general relativity and gauge field theory, one often encounters a claim, which may be called the , according to which “boundaries break diffeomorphism and gauge symmetries”. We argue that this statement has the same conceptual structure as the , and is thus likewise defused by the : We show that the boundary problem dissolves once it is understood that a , thus its boundary, is and . This insight can be technically implemented via the dressing field method, a systematic tool to exhibit the gauge-invariant content of general-relativistic gauge field theories, whereby physical field-theoretical degrees of freedom co-define each other and define, coordinatize, the . We illustrate our claim with a simple application to the case of general relativity.