Mathematics Colloquia and Seminars
Contact Geometry and Quantum MechanicsQMAP Seminar
|Speaker:||Andrew Waldron, Davis|
|Start time:||Fri, Oct 13 2017, 1:30PM|
We present a generally covariant approach to quantum mechanics. Generalized positions, momenta and time variables are treated as coordinates on a fundamental “phase-spacetime” manifold. Dynamics are encoded by giving phase-spacetime a contact structure. BRST quantization then yields a physical Hilbert space whose elements satisfy a parallel transport equation on a certain vector bundle over phase-spacetime. The inner product of solutions both reproduces and generalizes the Wigner functions of standard quantum mechanics.