Quantum Field Theory on Noncommutative Spaces

TL;DR

This paper provides a comprehensive, pedagogical overview of noncommutative quantum field theory, highlighting its connections to string theory and gravity, and exploring key mathematical and physical properties.

Contribution

It offers a self-contained introduction to noncommutative QFT, covering advanced topics like Morita equivalences and noncommutative gauge theories, with insights into their mathematical structure.

Findings

Analysis of UV/IR mixing phenomena

Development of noncommutative Yang-Mills theory models

Explanation of Morita equivalences in gauge theories

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.