Title: Deformation quantization of surjective submersions and principal fibre bundles
Authors: Bordemann, Martin ×
Neumaier, Nikolai
Waldmann, Stefan
Weiss, Stefan #
Issue Date: Feb-2010
Publisher: W. de Gruyter
Series Title: Journal für die Reine und Angewandte Mathematik (Crelle's Journal) vol:639 pages:1-38
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 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 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.
ISSN: 0075-4102
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Non-KU Leuven Association publications
× corresponding author
# (joint) last author

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