Noncommutative field theories from a deformation point of view. (English) Zbl 1163.53060

Waldmann, Stefan

Fauser, Bertfried (ed.) et al., Quantum field theory. Competitive models. Papers based on the presentations at the workshop on “Recent developments in quantum field theory”, Leipzig, Germany, July 20–22, 2007. Basel: Birkhäuser (ISBN 978-3-7643-8735-8/hbk). 117-135 (2009).

The author discusses the global geometry of noncommutative field theory from a deformation point of view. The space-times under consideration are deformations of classical space-time manifolds using star products. The matter fields are encoded in deformation quantizations of vector bundles over the classical space-time. For gauge theories, the author establishes a notion of deformation quantization of a principal line bundle and shows how the deformation of associated vector bundles can be obtained.
For the entire collection see [Zbl 1153.81002].

Reviewer: Benjamin Cahen (Metz)

MSC:

53D55	Deformation quantization, star products
58B34	Noncommutative geometry (à la Connes)
81T75	Noncommutative geometry methods in quantum field theory

Keywords:

noncommutative field theory; deformation quantization; principal bundles; locally noncommutative space-time