On Quantum-Geometric Connections and Propagators in Curved Spacetime
Eduard Prugovecki (Department of Mathematics, University of Toronto,, Toronto, ON, Canada)
TL;DR
This paper develops a framework for quantum connections and propagators in curved spacetime, ensuring gauge invariance and compatibility with relativity, with explicit methods for cosmological models.
Contribution
It introduces quantum connections in Poincare gauge invariant Hilbert bundles and derives path-integral propagator expressions in curved spacetimes.
Findings
Quantum connections satisfy the strong equivalence principle.
Path-integral propagators are Poincare gauge covariant.
Explicit computation method for Robertson-Walker spacetimes.
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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