On Quantum-Geometric Connections and Propagators in Curved Spacetime

Details On Quantum-Geometric Connections and Propagators in Curved Spacetime On Quantum-Geometric Connections and Propagators in Curved Spacetime

1995-10-04

arxiv.org/abs/gr-qc/9510007v1

Class.Quant.Grav. 13 (1996) 1007-1022

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Converted from a Mac-Word file to postscript for submission. The author may be reached directly via the above address, or at:

Scientific paper

10.1088/0264-9381/13/5/017

The basic properties of Poincare gauge invariant Hilbert bundles over Lorentzian manifolds are derived. Quantum connections are introduced in such bundles, which govern a parallel transport that is shown to satisfy the strong equivalence principle in the quantum regime. Path-integral expressions are presented for boson propagators in Hilbert bundles over globally hyperbolic curved spacetimes. Their Poincare gauge covariance is proven, and their special relativistic limit is examined. A method for explicitly computing such propagators is presented for the case of cosmological models with Robertson-Walker metric.

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