Noncommutative field theories from a deformation point of view

Details Noncommutative field theories from a deformation point of view Noncommutative field theories from a deformation point of view

2007-10-11

arxiv.org/abs/0710.2140v1

Mathematics

Quantum Algebra

19 pages. Contribution to the Proceedings of the Leipzig Conference "Recent Developments in Quantum Field Theory"

Scientific paper

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.

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