September 2001, Revised January 2003 | Richard J. Szabo
This chapter provides a pedagogical and self-contained introduction to noncommutative quantum field theory, with a focus on its connections to string theory and gravity. It covers topics such as the Weyl-Wigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative Yang-Mills theory on infinite space and 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. The chapter also briefly explains some mathematical ideas and techniques from noncommutative geometry. The historical context of spacetime noncommutativity, including evidence from quantum mechanics, string theory, and strong magnetic fields, is discussed. The chapter concludes with an outline of the major topics covered and references to additional resources.This chapter provides a pedagogical and self-contained introduction to noncommutative quantum field theory, with a focus on its connections to string theory and gravity. It covers topics such as the Weyl-Wigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative Yang-Mills theory on infinite space and 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. The chapter also briefly explains some mathematical ideas and techniques from noncommutative geometry. The historical context of spacetime noncommutativity, including evidence from quantum mechanics, string theory, and strong magnetic fields, is discussed. The chapter concludes with an outline of the major topics covered and references to additional resources.