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On Parallel Transport in Quantum Bundles over Robertson-Walker Spacetimes

James Coleman
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Abstract

A recently-developed theory of quantum general relativity provides a propagator for free-falling particles in curved spacetimes. These propagators are constructed by parallel-transporting quantum states within a quantum bundle associated to the Poincare frame bundle. We consider such parallel transport in the case that the spacetime is a classical Robertson-Walker universe. An explicit integral formula is developed which expresses the propagators for parallel transport between any two points of such a spacetime. The integrals in this formula are evaluated in closed form for a particular spatially-flat model.

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James Coleman. 1996-12-03. On Parallel Transport in Quantum Bundles over Robertson-Walker Spacetimes. https://arxiv.org/abs/gr-qc/9605067

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