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

2024/05/27 by Joshua Lackman, Lackman, Joshua
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Algebra (math.QA) #Quantum Mechanics and Applications #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2405.17273

openalex publication_date 2024/05/27 · openalex created_date 2024/05/29 · openalex updated_date 2026/07/28

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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