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

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.

Latex, 27 pages, added material on the `covariant' version of Poisson brackets. We explicitly define the extended history space in which both the Dirac algebra and the diffeomorphisms group are represented

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• Approaching the Problem of Time with a Combined Semiclassical-Records-Histories Scheme
• Poincare' invariance for continuous-time histories
• Generally covariant theories: the Noether obstruction for realizing certain space-time diffeomorphisms in phase space
• On the Semiclassical Approach to Quantum Cosmology
• Diffeomorphisms as Symplectomorphisms in History Phase Space: Bosonic String Model
• Covariance and Time Regained in Canonical General Relativity
• The role of phase space geometry in Heisenberg's uncertainty relation
• Histories Electromagnetism
• Quantum vs stochastic processes and the role of complex numbers
• BRST Quantisation of Histories Electrodynamics