Noncommutative field theory

@article{Douglas2001NoncommutativeFT,
  title={Noncommutative field theory},
  author={Michael R. Douglas and Nikita A. Nekrasov},
  journal={Reviews of Modern Physics},
  year={2001},
  volume={73},
  pages={977-1029}
}
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. 

Figures from this paper

Noncommutative Field Theory

We propose noncommutative space-time and a method to construct noncommutative field theory in terms of a covariant ★-product Moyal algebra and to study those physical and mathematical consequences.

RENORMALIZATION OF NONCOMMUTATIVE QUANTUM FIELD THEORY

We recall some models for noncommutative space-time and discuss quantum field theories on these deformed spaces. We discribe the IR/UV mixing disease, which implies nonrenormalizability for a large

Comments on noncommutative field theories

We discuss some aspects of noncommutative quantum field theories obtained from the Seiberg-Witten limit of string theories in the presence of an external B-field. General properties of these theories

Twists of quantum groups and noncommutative field theory

We discuss the role of quantum universal enveloping algebras of symmetries in constructing the noncommutative geometry of space-time and the corresponding field theory. It is shown that in the

Quantum field theory on noncommutative spaces

This survey tries to give a rigorous definition of Euclidean quantum field theory on a fairly large class of noncommutative geometries, namely nuclear AF Fréchet algebras. After a review of

D-Branes in Noncommutative Field Theory

A mathematical introduction to the classical solutions of noncommutative field theory is presented, with emphasis on how they may be understood as states of D-branes in Type II superstring theory.

Noncommutative field theory

Noncommutative field theories present many surprising properties. As a consequence of the noncommutativity, high momentum modes do not decouple from the physics at large distances leading to the
...

References

SHOWING 1-10 OF 276 REFERENCES

Noncommutative Tachyons And String Field Theory

It has been shown recently that by turning on a large noncommutativity parameter, the description of tachyon condensation in string theory can be drastically simplified. We reconsider these issues

Evidence for winding states in noncommutative quantum field theory

We study noncommutative field theories at finite temperature to learn more about the degrees of freedom in the non-planar sector of these systems. We find evidence for winding states. At temperatures

Noncommutative field theory and Lorentz violation.

Any realistic noncommutative theory is found to be physically equivalent to a subset of a general Lorentz-violating standard-model extension involving ordinary fields.

Remarks on Time-Space Noncommutative Field Theories

We propose a physical interpretation of the perturbative breakdown of unitarity in time-like non-commutative field theories in terms of production of tachyonic particles. These particles may be

SPACE-TIME UNCERTAINTY AND NONCOMMUTATIVITY IN STRING THEORY

We analyze the nature of space-time nonlocality in string theory. After giving a brief overview on the conjecture of the space-time uncertainty principle, a (semi-classical) reformulation of string

Divergencies in a field theory on quantum space

Running couplings and triviality of field theories on noncommutative spaces

We examine the issue of renormalizability of asymptotically free field theories on noncommutative spaces. As an example, we solve the noncommutative $O(N)$ invariant Gross-Neveu model at large N. On

Noncommutative perturbation in superspace

Topological quantum field theory

A twisted version of four dimensional supersymmetric gauge theory is formulated. The model, which refines a nonrelativistic treatment by Atiyah, appears to underlie many recent developments in
...