Quantum field theory on noncommutative spaces. (English) Zbl 1042.81581

Szabo, Richard J.

Phys. Rep. 378, No. 4, 207-299 (2003).

A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative Yang-Mills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an in-depth study of the gauge group of noncommutative Yang-Mills theory. Some of the more mathematical ideas and techniques of noncommutative geometry are also briefly explained.

MSC:

81T75

Noncommutative geometry methods in quantum field theory

Keywords:

Weyl-Wigner correspondence; Feynman diagrams; UV/IR mixing

References:

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