Contact geometry and quantum mechanics

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 make...

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Bibliographic Details
Published inPhysics letters. B Vol. 781; pp. 312 - 315
Main Authors Herczeg, Gabriel, Waldron, Andrew
Format Journal Article
LanguageEnglish
Published Elsevier B.V 10.06.2018
Elsevier
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Summary: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.
ISSN:0370-2693
1873-2445
DOI:10.1016/j.physletb.2018.04.008