A Groupoid Approach to Quantization

Details A Groupoid Approach to Quantization A Groupoid Approach to Quantization

2006-12-13

arxiv.org/abs/math/0612363v3

Mathematics

Symplectic Geometry

60 pages. V3: Minor corrections including Def 4.4. Added details in sections 6.1 and 8.2. Additional references. Some signs ch

Scientific paper

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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