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