Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1995-06-20
Class.Quant.Grav. 13 (1996) 611-632
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
25 pages, Plain TeX, harvmac/lanlmac
Scientific paper
10.1088/0264-9381/13/4/004
We study the Hilbert bundle description of stochastic quantum mechanics in curved spacetime developed by Prugove\v{c}ki, which gives a powerful new framework for exploring the quantum mechanical propagation of states in curved spacetime. We concentrate on the quantum transport law in the bundle, specifically on the information which can be obtained from the flat space limit. We give a detailed proof that quantum transport coincides with parallel transport in the bundle in this limit, confirming statements of Prugove\v{c}ki. We furthermore show that the quantum-geometric propagator in curved spacetime proposed by Prugove\v{c}ki, yielding a Feynman path integral-like formula involving integrations over intermediate phase space variables, is Poincar\'e gauge covariant (i.e.$\!$ is gauge invariant except for transformations at the endpoints of the path) provided the integration measure is interpreted as a ``contact point measure'' in the soldered stochastic phase space bundle raised over curved spacetime.
Drechsler Wolfgang
Tuckey Philip A.
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