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A Derivation of Geometric Quantization via Feynman's Path Integral on Phase Space
Published 27 May 2024 in math.SG, hep-th, math-ph, math.MP, and math.QA | (2405.17273v1)
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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