Abelian connection in Fedosov deformation quantization. I. The 2-dimensional phase space

TL;DR

This paper explores the properties of Abelian connections within Fedosov deformation quantization, focusing on the 2-dimensional phase space, and establishes criteria for their formal series representations.

Contribution

It introduces a definition and criterion for finite formal series of Abelian connections and proves that in 2D cases, these connections are infinite formal series.

Findings

Abelian connections are generally infinite formal series in 2D.

Criteria for finite formal series of Abelian connections are established.

Properties of Abelian connections in Fedosov deformation quantization are analyzed.

Abstract

General properties of an Abelian connection in Fedosov deformation quantization are investigated. Definition and criterion of being a finite formal series for an Abelian connection are presented. A proof that in 2-dimensional (2-D) case the Abelian connection is an ifinite formal series is done.