Geometro-Stochastic Quantization and Quantum Geometry

Eduard Prugovečki
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Eduard Prugovečki: University of Toronto, Department of Mathematics

A chapter in Quantization, Coherent States, and Complex Structures, 1995, pp 87-102 from Springer

Abstract: Abstract The most basic features of the geometro-stochastic method of quantization are outlined in the nonrelativistic and special relativistic regime. Their adaptation to the general relativistic regime leads to the replacement of the classical frame bundles, which underlie the formulation of parallel transport in classical general relativity, with quantum frame bundles. This gives rise to quantum geometries for quantum field theory in curved spacetime, in which quantum frames take over the role played by complete sets of observables in conventional quantum theory. The ensuing quantum-geometric mode of propagation in general relativistic quantum bundles is implemented by path integration methods based on parallel transport along broken paths consisting of arcs of geodesics of the Levi-Civita connection, and can be further extrapolated to a geometric formulation of quantum gravity.

Keywords: Parallel Transport; Quantum Geometry; Lorentz Frame; Poincare Group; Classical General Relativity (search for similar items in EconPapers)
Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-1060-8_10

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DOI: 10.1007/978-1-4899-1060-8_10

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