Phase Space Geometry in Classical and Quantum Mechanics

Details Phase Space Geometry in Classical and Quantum Mechanics Phase Space Geometry in Classical and Quantum Mechanics

2001-12-02

arxiv.org/abs/quant-ph/0112010v1

Physics

Quantum Physics

LaTeX, 16 pages, no figures

Scientific paper

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.

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