Contact Geometry and Quantum Mechanics

Abstract

We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes quantization into a purely geometric flatness condition. This makes quantum mechanics purely geometric, and possibly even topological. Our approach is especially useful for time-dependent problems and systems subject to ambiguities in choices of clock or observer. As a byproduct, we give a derivation and generalization of the Wigner functions of standard quantum mechanics.

arXiv comment7 pages, 1 figure, LaTeX, references added, journal version

References in corpus (11)

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Cited by in corpus (11)

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• Quantum to classical transition in the Hořava-Lifshitz quantum cosmology
• Contact Quantization: Quantum Mechanics = Parallel transport
• Induced $C^{\ast }$-complexes in metaplectic geometry
• On toral posets and contact Lie algebras
• The Quantum Darboux Theorem,
• Cartan Connection for Schrödinger equation. The nature of vacuum
• Dynamical Quantization of Contact Structures