Boundary structure of the standard model coupled to gravity

TL;DR

This paper describes the structure of the phase space in the standard model coupled to gravity, using symplectic reduction and BFV formalism for different boundary types, and explores Poisson brackets of functionals.

Contribution

It provides a detailed description of the reduced phase space for the standard model coupled to gravity, including boundary-specific methods and new results on Poisson brackets.

Findings

Reduced phase space for space/time-like boundaries via symplectic reduction and BFV formalism.

Reduced phase space for light-like boundaries as a symplectic reduction with constraints.

New results on Poisson brackets of sums of functionals.

Abstract

In this article a description of the reduced phase space of the standard model coupled to gravity is given. For space or time-like boundaries this is achieved as the reduction of a symplectic space with respect to a coisotropic submanifold and with the BFV formalism. For light-like boundaries the reduced phase space is described as the reduction of a symplectic manifold with respect to a set of constraints. Some results about the Poisson brackets of sums of functionals are also proved.