Deformation Quantization of Surjective Submersions and Principal Fibre Bundles
Abstract
In this paper we establish a notion of deformation quantization of a surjective submersion which is specialized further to the case of a principal fibre bundle: the functions on the total space are deformed into a right module for the star product algebra of the functions on the base manifold. In case of a principal fibre bundle we require in addition invariance under the principal action. We prove existence and uniqueness of such deformations. The commutant within all differential operators on the total space is computed and gives a deformation of the algebra of vertical differential operators. Applications to noncommutative gauge field theories and phase space reduction of star products are discussed.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.2965
 Bibcode:
 2007arXiv0711.2965B
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematical Physics;
 53D55
 EPrint:
 32 pages, typos corrected