Can I read Deformation Quantization of Surjective Submersions and Principal Fibre Bundles on EtoBox?

Deformation Quantization of Surjective Submersions and Principal Fibre Bundles by Martin Bordemann; Nikolai Neumaier; Stefan Waldmann; Stefan Weiß is a Mathematics article available to read on EtoBox.

What is Deformation Quantization of Surjective Submersions and Principal Fibre Bundles about?

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 the case of a principal fibre bundle we additionally require invariance under the principal action. We prove existence and uniqueness of such deformations. The commutant within all di¤erential operators on the total space is computed and gives a deformation of the algebra of vertical di¤erential operators. Applications to noncommutative gauge field theories and phase space reduction of star products are discussed. Example 1.2. Consider the Hopf fibration p : S 3 ! S 2 , which is an S 1 -principal bundle, and a symplectic Poisson structure p S 2 on the 2-sphere S 2 . Then there is no Poisson structure on S 3 making p a Poisson map. Indeed, it is easy to see that the symplectic leaves of ðS 3 ; p S 3 Þ have to be 2-dimensional and the restriction of p to one leaf is still surjective. Thus the leaf covers S 2 whence it is di¤eomorphic to S 2 via p. But this immediately gives a global section

Who reads Deformation Quantization of Surjective Submersions and Principal Fibre Bundles?

Author

Martin Bordemann; Nikolai Neumaier; Stefan Waldmann; Stefan Weiß

Publisher

Walter de Gruyter GmbH

Published

2010

Field

Mathematics (Physical Sciences)