A Derivation of Geometric Quantization via Feynman's Path Integral on Phase Space

Abstract

We derive the geometric quantization program of symplectic manifolds, in the sense of both Kostant-Souriau and Weinstein, from Feynman's path integral formulation on phase space. The state space we use contains states with negative norm and polarized sections determine a Hilbert space. We discuss ambiguities in the definition of path integrals arising from the distinct Riemann sum prescriptions and its consequence on the quantization of symplectomorphisms.

arXiv comment10 pages plus appendix and references