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arXiv · gr-qc/9510007

On Quantum-Geometric Connections and Propagators in Curved Spacetime

Eduard Prugovecki
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Abstract

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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Eduard Prugovecki. 1995-10-04. On Quantum-Geometric Connections and Propagators in Curved Spacetime. https://doi.org/10.1088/0264-9381%2F13%2F5%2F017

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