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Contact Geometry and Quantum Mechanics

QMAP Seminar

Speaker: Andrew Waldron, Davis
Location: 2112 MSB
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.