The Fedosov deformation quantization for some induced symplectic connection

TL;DR

This paper explores Fedosov deformation quantization on cotangent bundles with symplectic connections induced by linear symmetric connections, providing a global construction, examples, and analysis of the resulting *-product.

Contribution

It introduces a global construction of symplectic connections induced by base space connections and analyzes their impact on deformation quantization.

Findings

Constructed a global symplectic connection model

Analyzed properties of the *-product for induced connections

Provided examples of induced symplectic connections

Abstract

The Fedosov deformation quantization on a cotangent bundle with a symplectic connection induced by some linear symmetric connection on the base space is considered. A global construction of the symplectic homogeneous connection on the cotangent bundle modelled on the linear symmetric connection from the base space is proposed. Examples of the induced symplectic connection are given. A detailed analysis of the Abelian connection and flat sections representing special types of functions for this kind of symplectic connection is presented. Some properties of the *-product determined by the induced symplectic connection are shown.