On an Axiomatization of Path Integral Quantization and its Equivalence to Berezin's Quantization

2024/10/03 by Joshua Lackman, Lackman, Joshua
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2410.02739

openalex publication_date 2024/10/03 · openalex created_date 2024/10/30 · openalex updated_date 2026/07/28

Abstract

We axiomatize path integral quantization of symplectic manifolds. We prove that this path integral formulation of quantization is equivalent to an abstract operator formulation, ie. abstract coherent state (or Berezin) quantization. We use the corresponding path integral of Poisson manifolds to quantize all complete Riemann surfaces of constant non\unicodex2013positive curvature and some Poisson structures on the sphere.

Related

• A Mathematical Definition of Path Integrals on Symplectic Manifolds
• Quantization of Holomorphic Symplectic Manifolds: Analytic Continuation of Path Integrals and Coherent States
• A Derivation of Geometric Quantization via Feynman's Path Integral on Phase Space
• The Berezin-Simon quantization for Kähler manifolds and their path integral representations
• A Canonical Quantization of Poisson Manifolds: a 2-Groupoid Scheme