Deformation quantization of Poisson manifolds in the derivative expansion

TL;DR

This paper explores deformation quantization of Poisson manifolds using a derivative expansion approach, constructing a Lie group that captures second-order deformations of the Poisson algebra.

Contribution

It introduces a novel derivative expansion method for deformation quantization and constructs a Lie group representing second-order deformations.

Findings

Constructed a Lie group for Poisson bracket algebra

Developed a second-order deformation in derivative expansion

Provided a framework for quantization in Poisson geometry

Abstract

Deformation quantization of Poisson manifolds is studied within the framework of an expansion in powers of derivatives of Poisson structures. We construct the Lie group associated with a Poisson bracket algebra which defines a second order deformation in the derivative expansion.