General relativity histories theory II: Invariance groups

Details General relativity histories theory II: Invariance groups General relativity histories theory II: Invariance groups

2003-06-09

arxiv.org/abs/gr-qc/0306036v1

Class.Quant.Grav. 21 (2004) 631

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, submitted to Class. Quant. Grav

Scientific paper

10.1088/0264-9381/21/2/021

We show in detail how the histories description of general relativity carries representations of both the spacetime diffeomorphisms group and the Dirac algebra of constraints. We show that the introduction of metric-dependent equivariant foliations leads to the crucial result that the canonical constraints are invariant under the action of spacetime diffeomorphisms. Furthermore, there exists a representation of the group of generalised spacetime mappings that are functionals of the four-metric: this is a spacetime analogue of the group originally defined by Bergmann and Komar in the context of the canonical formulation of general relativity. Finally, we discuss the possible directions for the quantization of gravity in histories theory.

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