Noncommutative field theory

By Michael R Douglas, N. Nekrasov. 2001

1,902 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ff829c1cab7a67ce29a3e6216b9b516d6929750f

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Citations in the corpus

Vanishing of beta function of non-commutative Φ 4 4 theory to all orders (2006, background): “I Introduction Non commutative (NC) quantum field theory (QFT) may be important for physics beyond the standard model and for understanding the quantum Hall effect [1].”
Modern Tests of Lorentz Invariance (2005, methodology): “Further information on copyright is given at http://relativity.livingreviews.org/About/copyright.html For permission to reproduce the article please contact livrev@aei.mpg.de.”
New realizations of Lie algebra kappa-deformed Euclidean space (2006, background): “Infinitely many realizations in terms of commuting coordinates are constructed and a corresponding star product is found for each of them.”
Symmetry, gravity and noncommutativity (2006, methodology): “ill then discuss a manner in which these models can serve as gauge theories of gravitation. More details of noncommutative Yang-Mills theory in the context of this section can be found in the reviews [51, 114]. 3.1 Star-Gauge Symmetry Let A= Ai(x) dxibe a U(N) gauge ﬁeld. The action for noncommutati”
D-Branes, Tachyons, and String Field Theory (2003, background): “…example of a situation where adding an infinite number of apparently nonrenormalizable terms to a field theory action leads to a sensible modification of quantum field theory (for a review of noncommutative field theory and its connection to string theory, see Douglas and Nekrasov [21]).”
Deformations of superconformal theories (2016, background): “Here we briefly mention a well-studied example, which arises in the context of non-commutative gauge theories (see [80] and references therein).”
What is geometry in quantum theory (2004, background): “Noncommutative field theory also can be treated in this manner [138, 139], though the bracket of space coordinates [x, x ] = iθ in this theory is also restarted from Moyal’s star product x⋆x [138, 140].”