Edge modes as reference frames and boundary actions from post-selection

Understand

We introduce a general framework realizing edge modes in (classical) gauge field theory as dynamical reference frames, an often suggested interpretation that we make entirely explicit.

• We focus on a bounded region $M$ with a co-dimension one time-like boundary $\Gamma$, which we embed in a global spacetime.
• Taking as input a variational principle at the global level, we develop a systematic formalism inducing consistent variational principles (and in particular, boundary actions) for the subregion $M$.
• This relies on a post-selection procedure on $\Gamma$, which isolates the subsector of the global theory compatible with a general choice of gauge-invariant boundary conditions for the dynamics in $M$.