How to calculate the Fedosov star--product (Exercices de style)

Abstract

This is an expository note on Fedosov's construction of deformation quantization. Given a symplectic manifold and a connection on it, we show how to calculate the star-product step by step. We draw simple diagrams to solve the recursive equations for the Fedosov connection and for flat sections of the Weyl algebra bundle corresponding to functions. We also reflect on the differences of symplectic and Riemannian geometries.