Seminar Contact Geometry and Quantum Mechanics

Contatto di riferimento: Barbara Simoni

Partecipanti: Prof. Andrew Waldron: UC, Davis

Abstract: We present a generally covariant approach to quantum mechanics. Generalized positions, momenta and TIME are treated on the same footing as coordinates on a fundamental “phase-spacetime” manifold. Dynamics are encoded by giving phase-spacetime a contact structure. BRST quantization yields a physical Hilbert space described by a Hilbert bundle over phase-spacetime. Inner products of solutions then both reproduces and generalizes the Wigner functions of standard quantum mechanics. In this picture "quantization = finding a flat connection" and “quantum evolution = parallel transport".