From topological field theory to deformation quantization and reduction

TL;DR

This paper explores the quantization of 2D topological field theories and their applications to deformation quantization of Poisson manifolds and submanifold reduction, using the Batalin-Vilkovisky formalism.

Contribution

It introduces a functional-integral approach to quantize topological field theories and applies it to deformation quantization and reduction problems.

Findings

Quantization method for 2D topological field theories

Applications to deformation quantization of Poisson manifolds

Reduction of specific submanifolds

Abstract

This note describes the functional-integral quantization of two-dimensional topological field theories together with applications to problems in deformation quantization of Poisson manifolds and reduction of certain submanifolds. A brief introduction to smooth graded manifolds and to the Batalin-Vilkovisky formalism is included.