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arXiv · 1709.04557

Contact Geometry and Quantum Mechanics

Gabriel Herczeg·Andrew Waldron
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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.

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Gabriel Herczeg, Andrew Waldron. 2017-09-13. Contact Geometry and Quantum Mechanics. https://doi.org/10.1016/j.physletb.2018.04.008

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