Contact geometry and quantum mechanics

• Main Authors: Gabriel Herczeg, Andrew Waldron
• Format: Article
• Language: English
• Published: Elsevier 2018-06-01
• Series: Physics Letters B
• Online Access: http://www.sciencedirect.com/science/article/pii/S0370269318302922

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.