Phase Space Geometry in Classical and Quantum Mechanics

Abstract

Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the symplectic manifold of classical phase space with a Riemannian metric is sufficient for describing quantum mechanics. In particular, using such spaces, a fully satisfactory geometric version of quantization will be developed and described.

LaTeX, 16 pages, no figures

Cited by in corpus (6)

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• Enhanced quantization on the circle
• Phase space holography with no strings attached
• The Klauder-Daubechies Construction of the Phase Space Path Integral and the Harmonic Oscillator
• Classical tensors from quantum states
• A Deformation of Quantum Dynamics through the Phase Space Path Integral