Covariant Phase Space Formulation of Parametrized Field Theories

TL;DR

This paper explores the covariant phase space approach to parametrized field theories, addressing how to represent spacetime diffeomorphisms, construct observables, and relate canonical and covariant formulations, with implications for general relativity.

Contribution

It develops a covariant phase space framework for parametrized field theories, clarifying the representation of diffeomorphisms and the construction of observables.

Findings

Established a phase space representation of spacetime diffeomorphisms.

Connected canonical and covariant phase space structures.

Provided insights relevant to general relativity.

Abstract

Parametrized field theories, which are generally covariant versions of ordinary field theories, are studied from the point of view of the covariant phase space: the space of solutions of the field equations equipped with a canonical (pre)symplectic structure. Motivated by issues arising in general relativity, we focus on: phase space representations of the spacetime diffeomorphism group, construction of observables, and the relationship between the canonical and covariant phase spaces.