Noncommutative field theory

Douglas M.R., Nekrasov N.A.

This article reviews 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 nowknown to emerge from limits of M theory and string theory and to describe quantum Hall states. Inthe last few years they have been studied intensively, and many qualitatively new phenomena havebeen discovered, on both the classical and the quantum level.