Contact Geometry and Quantum Mechanics

Understand

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.