Abstract. In this paper we show in detail how the histories description of general relativity carries representations of both the spacetime diffeomorphism 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 generalized spacetime mappings that are functionals of the 4-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.

PACS number: 04.60.Gw

Print publication: Issue 2 (21 January 2004)
Received 1 June 2003
Published 10 December 2003