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arXiv · 2405.17273

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

Joshua Lackman
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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.

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Joshua Lackman. 2024-05-27. A Derivation of Geometric Quantization via Feynman's Path Integral on Phase Space. https://arxiv.org/abs/2405.17273

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