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On the Space-Time Geometry of Quantum Systems
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abstract
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 $\mbox{SO}(3)$ and $\mbox{U}(1)$-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.
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Cited by 1 Pith paper
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Local description of S-matrix in quantum field theory in curved spacetime using Riemann-normal coordinate
A local S-matrix is constructed in curved spacetime using Riemann-normal coordinates, yielding curvature-dependent scattering amplitudes and cross-sections.
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