Deformation Quantization : an introduction

Notes for an Introduction to Kontsevich’s quantization theorem

In these notes, we present Kontsevich’s theorem on the deformation quantization of Poisson manifolds, his formality theorem and Tamarkin’s algebraic version of the formality theorem. We also introduce the necessary material from deformation theory.

Deformation Quantization - a Brief Survey

Quantization is, most broadly, the process of forming a quantum mechanical system starting from a classical mechanical one. See (Be) for an early attempt to obtain a general definition of quantization. (AbM) also provides an introductory account of the subject. There are various methods of quantization; see (BW) for a general introduction to the geometry of quantization, and a specific geometri...

an introduction to DEFORMATION QUANTIZATION after Kontsevich

States and representations in deformation quantization

In this review we discuss various aspects of representation theory in deformation quantization starting with a detailed introduction to the concepts of states as positive functionals and the GNS construction. But also Rieffel induction of representations as well as strong Morita equivalence, the Dirac monopole and the strong Picard groupoid are discussed. E-mail: [email protected]...

An operadic approach to deformation quantization of compatible Poisson brackets

An analogue of the Livernet–Loday operad for two compatible brackets, which is a flat deformation of the bi-Hamiltonian operad is constructed. The Livernet–Loday operad can be used to define ⋆-products and deformation quantization for Poisson structures. The constructed operad is used in the same way, introducing a definition of operadic deformation quantization of compatible Poisson structures...