1994/12/05 by Dirk Graudenz, Graudenz, Dirk
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.gr-qc/9412013
15 pages (LaTeX); figures are included via epsfig; the corresponding postscript files are uuencoded; AMS-fonts are needed
arxiv created 1994/12/05 · openalex publication_date 1994/12/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe the time evolution of quantum systems in a classical background space-time by means of a covariant derivative in an infinite dimensional vector bundle. The corresponding parallel transport operator along a timelike curve \cC is interpreted as the time evolution operator of an observer moving along \cC. The holonomy group of the connection, which can be interpreted as a group of local symmetry transformations, and the set of observables have to satisfy certain consistency conditions. Two examples related to local SO(3) and U(1)-symmetries, respectively, are discussed in detail. The theory developed in this paper may also be useful to analyze situations where the underlying space-time manifold has closed timelike curves.