Spacetime boundaries do not break diffeomorphism and gauge symmetries

TL;DR

The work demonstrates that spacetime boundaries do not break diffeomorphism or gauge symmetries when physical content is expressed relationally. It implements this insight with the Dressing Field Method, which constructs gauge- and diffeomorphism-invariant variables and dressed regions, thereby making the generalized point-coincidence structure explicit. The authors prove, both abstractly and computationally, the invariance of dressed metrics and regions in GR, and illustrate the approach with scalar coordinatization of GR via matter fields. The framework dissolves not only the boundary problem but also offers a relational route to address the problem of time and hints at a path toward Relational Quantization in quantum gravity.

Abstract

In General Relativity and gauge field theory, one often encounters a claim, which may be called the boundary problem, according to which "boundaries break diffeomorphism and gauge symmetries". We argue that this statement has the same conceptual structure as the hole argument, and is thus likewise defused by the point-coincidence argument: We show that the boundary problem dissolves once it is understood that a physical region, thus its boundary, is relationally and invariantly defined. 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 physical spacetime. We illustrate our claim with a simple application to the case of General Relativity.