English

On quantum and parallel transport in a Hilbert bundle over spacetime

General Relativity and Quantum Cosmology 2009-10-28 v3

Abstract

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.

Keywords

Cite

@article{arxiv.gr-qc/9506039,
  title  = {On quantum and parallel transport in a Hilbert bundle over spacetime},
  author = {W. Drechsler and Philip A. Tuckey},
  journal= {arXiv preprint arXiv:gr-qc/9506039},
  year   = {2009}
}

Comments

25 pages, Plain TeX, harvmac/lanlmac

R2 v1 2026-07-22T12:50:16.618Z