Partial and Complete Observables for Canonical General Relativity

TL;DR

This paper develops a method to compute Dirac observables in canonical general relativity using partial and complete observables, simplifying the process by focusing on a single constraint and connecting space-time and canonical invariants.

Contribution

It introduces a way to calculate Dirac observables with just one constraint by employing spatial diffeomorphism invariant Hamiltonian constraints, which can be made Abelian.

Findings

Can compute Dirac observables using a single constraint.

Introduces spatial diffeomorphism invariant Hamiltonian constraints.

Establishes a connection between space-time and canonical observables.

Abstract

In this work we will consider the concepts of partial and complete observables for canonical general relativity. These concepts provide a method to calculate Dirac observables. The central result of this work is that one can compute Dirac observables for general relativity by dealing with just one constraint. For this we have to introduce spatial diffeomorphism invariant Hamiltonian constraints. It will turn out that these can be made to be Abelian. Furthermore the methods outlined here provide a connection between observables in the space--time picture, i.e. quantities invariant under space--time diffeomorphisms, and Dirac observables in the canonical picture.