A perturbative approach to Dirac observables and their space-time algebra

TL;DR

This paper presents a perturbative scheme for calculating gauge invariant observables in general relativity, connecting linearized theory to full theory and exploring their algebraic and locality properties.

Contribution

It introduces a systematic approximation method for Dirac observables and analyzes their space-time algebra and locality in the context of general relativity.

Findings

First non-trivial gauge invariant correction calculated

Established connection between linearized and full general relativity observables

Explored the Poisson algebra and locality of space-time observables

Abstract

We introduce a general approximation scheme in order to calculate gauge invariant observables in the canonical formulation of general relativity. Using this scheme we will show how the observables and the dynamics of field theories on a fixed background or equivalently the observables of the linearized theory can be understood as an approximation to the observables in full general relativity. Gauge invariant corrections can be calculated up to an arbitrary high order and we will explicitly calculate the first non--trivial correction. Furthermore we will make a first investigation into the Poisson algebra between observables corresponding to fields at different space--time points and consider the locality properties of the observables.