Noncommutative Field Theory

TL;DR

This paper reviews noncommutative field theories, highlighting their origins from string theory and M theory, and discussing recent discoveries of new phenomena at classical and quantum levels.

Contribution

It provides a comprehensive overview of noncommutative field theories, including recent research developments and their physical implications.

Findings

Emergence from string and M theory limits

Application to quantum Hall states

Discovery of new classical and quantum phenomena

Abstract

We review the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory, and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, both on the classical and quantum level. To appear in Reviews of Modern Physics.