Global Non-perturbative Deformation Quantization of a Poisson Algebra

TL;DR

This paper introduces a novel approach to quantizing Poisson algebras by defining the quantum product as a geodesic on the manifold of associative products, offering a non-perturbative perspective.

Contribution

It proposes a new non-perturbative deformation quantization framework for Poisson algebras using geometric methods.

Findings

Defines a geodesic-based quantum product on the manifold of associative products

Provides a new perspective on non-perturbative quantization methods

Lays groundwork for further mathematical exploration of quantum deformations

Abstract

A proposed definition is given for the quantization of a Poisson algebra, taking the quantum product to be a geodesic on the manifold of associative products.