A Groupoid Approach to Quantization

2006/12/13 by Eli Hawkins, Hawkins, Eli · 1 citation
Mathematics · #22A22 #46L65 #53D17 #53D50 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.math/0612363

openalex publication_date 2006/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Many interesting C*-algebras can be viewed as quantizations of Poisson manifolds. I propose that a Poisson manifold may be quantized by a twisted polarized convolution C*-algebra of a symplectic groupoid. Toward this end, I define polarizations for Lie groupoids and sketch the construction of this algebra. A large number of examples show that this idea unifies previous geometric constructions, including geometric quantization of symplectic manifolds and the C*-algebra of a Lie groupoid.

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• The electromagnetic field in Poisson gauge theory: the groupoidal approach

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