On the Space-Time Geometry of Quantum Systems
نویسنده
چکیده
We describe the time evolution of quantum systems in a classical background spacetime by means of a covariant derivative in an infinite dimensional vector bundle. The corresponding parallel transport operator along a timelike curve C is interpreted as the time evolution operator of an observer moving along C. The holonomy group of the connection, which can be viewed 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. CERN-TH.7516/94 November 1994 ∗Electronic mail addresses: graudenz @ cernvm.cern.ch, i02gau @ dsyibm.desy.de
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