Comparison of Various Methods in Deformation Quantization

Project overview

Deformation quantization introduced by Bayen et al. is a formalization of the general idea of quantization of a classical mechanical system to a quantum mechanical system. In this formulation, a classical mechanical is characterized by a Poisson/symplectic structure, and a quantum mechanical system is characterized by a “star product” which is a formal deformation of the multiplication of smooth functions. Nowadays, there are several approaches to this subject. We are particularly interested in

• Kontsevich’s approach by formality theorem,

• Berezin-Toeplitz quantization

and their relationship.