A Ring-Theorist's Description of Fedosov Quantization

TL;DR

This paper provides an algebraic framework for Fedosov's deformation quantization of symplectic manifolds, emphasizing affine symplectic algebras to formalize the process.

Contribution

It offers a rigorous algebraic formulation of Fedosov's method, extending the understanding of deformation quantization in symplectic geometry.

Findings

Formal algebraic treatment of Fedosov's formulas

Extension of deformation quantization to affine symplectic algebras

Clarification of the algebraic structure underlying Fedosov's approach

Abstract

We present a formal, algebraic treatment of Fedosov's argument that the coordinate algebra of a symplectic manifold has a deformation quantization. His remarkable formulas are established in the context of affine symplectic algebras.