Quantum field theory on noncommutative spaces

Research output: Contribution to journalLiterature review

Abstract

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. © 2003 Elsevier Science B.V. All rights reserved.

Original languageEnglish
Pages (from-to)207-299
Number of pages93
JournalPhysics Reports
Volume378
Issue number4
DOIs
Publication statusPublished - May 2003

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Yang-Mills theory
Feynman diagrams
string theory
equivalence
gauge theory
gravitation
geometry

Cite this

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Quantum field theory on noncommutative spaces. / Szabo, Richard J.

In: Physics Reports, Vol. 378, No. 4, 05.2003, p. 207-299.

Research output: Contribution to journalLiterature review

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AB - 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. © 2003 Elsevier Science B.V. All rights reserved.

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