Abelian connection in Fedosov deformation quantization. I. The 2-dimensional phase space
Mathematical Physics
2007-12-31 v2 math.MP
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.
Cite
@article{arxiv.math-ph/0602063,
title = {Abelian connection in Fedosov deformation quantization. I. The 2-dimensional phase space},
author = {Jaromir Tosiek},
journal= {arXiv preprint arXiv:math-ph/0602063},
year = {2007}
}
Comments
13 pages; new formulation of the criterion, when the Abelian connection is a finite formal series, is proposed. Modified proof of the fact, that on 2-D symplectic space the Abelian correction is an infinite formal series, is shown. The part devoted to different symplectic connections generating the same Abelian correction, has been removed. It will be added to another paper