General relativity histories theory: Spacetime diffeomorphisms and the Dirac algebra of constraints

TL;DR

This paper demonstrates that in a phase-space histories formulation of canonical general relativity, representations of spacetime diffeomorphisms and the Dirac algebra naturally emerge, revealing a complex structure of time and symmetry similar to non-relativistic physics.

Contribution

It introduces a histories-based phase-space approach to general relativity where spacetime diffeomorphisms and the Dirac algebra are represented, highlighting novel time structures.

Findings

Representation of spacetime diffeomorphisms in histories theory

Emergence of the Dirac algebra in phase-space histories

Identification of two types of time translation in relativistic context

Abstract

We show that representations of the group of spacetime diffeomorphism and the Dirac algebra both arise in a phase-space histories version of canonical general relativity. This is the general-relativistic analogue of the novel time structure introduced previously in history theory: namely, the existence in non-relativistic physics of two types of time translation; and the existence in relativistic field theory of two distinct Poincare groups.