Edge modes as reference frames and boundary actions from post-selection
- URL: http://arxiv.org/abs/2109.06184v4
- Date: Thu, 3 Feb 2022 15:36:43 GMT
- Title: Edge modes as reference frames and boundary actions from post-selection
- Authors: Sylvain Carrozza and Philipp A. Hoehn
- Abstract summary: We introduce a general framework realizing edge modes in (classical) gauge field theory as dynamical reference frames.
We identify boundary symmetries as frame reorientations and show that they divide into three types, depending on the boundary conditions.
Our construction relies on the covariant phase space formalism, and is in principle applicable to any gauge (field) theory.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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 $M$. Crucially, the latter relate the
configuration fields on $\Gamma$ to a dynamical frame field carrying
information about the spacetime complement of $M$; as such, they may be
equivalently interpreted as frame-dressed or relational observables.
Generically, the external frame field keeps an imprint on the ensuing dynamics
for subregion $M$, where it materializes itself as a local field on the
time-like boundary $\Gamma$; in other words, an edge mode. We identify boundary
symmetries as frame reorientations and show that they divide into three types,
depending on the boundary conditions, that affect the physical status of the
edge modes. Our construction relies on the covariant phase space formalism, and
is in principle applicable to any gauge (field) theory. We illustrate it on
three standard examples: Maxwell, Abelian Chern-Simons and non-Abelian
Yang-Mills theories. In complement, we also analyze a mechanical toy-model to
connect our work with recent efforts on (quantum) reference frames.
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