Quantum Field Theory on Noncommutative Spaces

2001/09/30 by Richard J. Szabo · 3 citations
Physics and Astronomy · Mathematics · #hep-th #cond-mat #gr-qc #hep-lat #hep-ph #math-ph #math.MP #math.QA

paper · pdf · doi:10.1016/s0370-1573(03)00059-0

published as Phys.Rept.378:207-299,2003 · 111 pages LaTeX, 6 eps figures; Some material and discussions added for clarity, corrections done, references added; Final version to be published in Physics Reports

arxiv created 2003/01/23 · arxiv updated 2009/11/30

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.

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