Boundary structure of gauge and matter fields coupled to gravity

TL;DR

This paper analyzes the boundary structure of 3+1 dimensional gravity coupled with gauge and matter fields, using symplectic reduction and cohomological methods to describe the phase space.

Contribution

It provides a detailed cohomological BFV description of the boundary phase space for gravity coupled to gauge and matter fields.

Findings

Reduced phase space obtained via symplectic reduction.

Cohomological BFV description of the boundary structure.

Explicit treatment of gauge and matter field coupling.

Abstract

The boundary structure of $3+1$-dimensional gravity (in the Palatini-Cartan formalism) coupled to to gauge (Yang-Mills) and matter (scalar and spinorial) fields is described through the use of the Kijowski-Tulczijew construction. In particular, the reduced phase space is obtained as the reduction of a symplectic space by some first class constraints and a cohomological description (BFV) of it is presented.