Covariant gauge fixing and Kuchar decomposition

TL;DR

This paper explores the symplectic geometry of covariant models, defining gauge fixing and Kuchar decomposition to separate physical degrees of freedom from embeddings in a background spacetime.

Contribution

It provides a geometric framework for gauge fixing and Kuchar decomposition in covariant models with Bergmann-Komar symmetry, extending these concepts locally.

Findings

Defined gauge fixing geometrically at the constraint manifold

Established equivalence with background spacetime for each topological sector

Proved local extendability of gauge fixings and decompositions

Abstract

The symplectic geometry of a broad class of generally covariant models is studied. The class is restricted so that the gauge group of the models coincides with the Bergmann-Komar group and the analysis can focus on the general covariance. A geometrical definition of gauge fixing at the constraint manifold is given; it is equivalent to a definition of a background (spacetime) manifold for each topological sector of a model. Every gauge fixing defines a decomposition of the constraint manifold into the physical phase space and the space of embeddings of the Cauchy manifold into the background manifold (Kuchar decomposition). Extensions of every gauge fixing and the associated Kuchar decomposition to a neighbourhood of the constraint manifold are shown to exist.