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 …

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 …

A bstract We study the connection of Moyal deformations of self-dual gravity and self-dual
Yang-Mills theory to chiral higher-spin theories, and also to deformations of operator …

An introductory review to emergent noncommutative gravity within Yang–Mills matrix models
is presented. Spacetime is described as a noncommutative brane solution of the matrix …

We consider the standard model on a non-commutative space and expand the action in the
non-commutativity parameter θ^μν. No new particles are introduced; the structure group is …

We derive noncommutative multiparticle quantum mechanics from noncommutative
quantum field theory in the nonrelativistic limit. Particles of opposite charges are found to …

We review the present status of gauge theories built on various quantum space–times
described by noncommutative space–times. The mathematical tools and notions underlying …

Recent theoretical results have demonstrated that noncommutative geometries naturally
appear within the context of string or M theory. One consequence of this possibility is that …

A non-commutative version of the usual electro-weak theory is constructed. We discuss how
to overcome the two major problems:(1) although we can have non-commutative U …

It is natural to ask whether noncommutative geometry plays a role in four dimensional
physics. By performing explicit computations in various toy models, we show that quantum …