2007/10/11 by Waldmann, Stefan
#53D55 (Primary) #58B34 #81T75 (Secondary) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.0710.2140
In this review we discuss the global geometry of noncommutative field theories from a deformation point of view: The space-times under consideration are deformations of classical space-time manifolds using star products. Then matter fields are encoded in deformation quantizations of vector bundles over the classical space-time. For gauge theories we establish a notion of deformation quantization of a principal fiber bundle and show how the deformation of associated vector bundles can be obtained.