Deformation quantization from functional integrals

Cattaneo, A S (2005). Deformation quantization from functional integrals. In: Cattaneo, A S; Keller, B; Torossian, C; Bruguières, A. Déformation, quantification, théorie de Lie. Paris: Société Mathématique de France, 123-164.

Abstract

The aim of this Chapter is to explain how to obtain Kontsevich’s formula [7] from the perturbative computation of the functional integral of a topological ﬁeld theory
known as the Poisson sigma model. We start with an introduction to the perturbative evaluation of functional integrals. We describe next how to do it in the presence of
symmetries generated by the free action of a Lie algebra. This allows the full treatment of the Poisson sigma model for an affine Poisson structure. For the general case, we
refer to [5].

Abstract

The aim of this Chapter is to explain how to obtain Kontsevich’s formula [7] from the perturbative computation of the functional integral of a topological ﬁeld theory
known as the Poisson sigma model. We start with an introduction to the perturbative evaluation of functional integrals. We describe next how to do it in the presence of
symmetries generated by the free action of a Lie algebra. This allows the full treatment of the Poisson sigma model for an affine Poisson structure. For the general case, we
refer to [5].