Deformation Quantization

Abstract

In this course, we first introduce various mathematical quantizations: geometric quantization, deformation quantization and symbol calculus. Then, we study deformation quantization of a symplectic manifold: Hochschild cohomology, Deligne's classes and the classification of equivalence classes of deformation quantization, traces for star products, notions of invariance for star products. We shall furthermore describe Kontsevitch's formality theorem and its consequences for deformation quantization of Poisson manifolds.

Index

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