Physics Letters B (Jun 2018)

Contact geometry and quantum mechanics

  • Gabriel Herczeg,
  • Andrew Waldron

Journal volume & issue
Vol. 781
pp. 312 – 315

Abstract

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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.