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Noncommutative field theory
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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 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, on both the classical and the quantum level.
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“Other high energy models of spacetime structure, such as non-commutative field theory, do however explicitly contain Lorentz violation [98].”
From Modern Tests of Lorentz Invariance (2005) · cites this paper as [98]
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Estrada-Jiménez, S., García‐Compeán, H., Obregón, O., & Ramírez, C. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.78.124008 · Cited by 26
Energy crisis or a new soliton in the noncommutative CP(1) model?
Ghosh, S. (2003) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2003.08.016 · Cited by 26
Bosonization in the noncommutative plane
Ghosh, S. (2003) · Physics Letters B · doi:10.1016/s0370-2693(03)00590-2 · Cited by 26
Telltale traces of U(1) fields in noncommutative standard model extensions
Jaeckel, J., Khoze, V. V., & Ringwald, A. (2006) · Journal of High Energy Physics · doi:10.1088/1126-6708/2006/02/028 · Cited by 26
Non-commutative multi-dimensional cosmology
Khosravi, N., Jalalzadeh, S., & Sepangi, H. R. (2006) · Journal of High Energy Physics · doi:10.1088/1126-6708/2006/01/134 · Cited by 26
UV/IR mixing and the Goldstone theorem in noncommutative field theory
Ruiz, F. R. (2002) · Nuclear Physics B · doi:10.1016/s0550-3213(02)00447-9 · Cited by 26
Open Wilson lines and group theory of noncommutative Yang-Mills theory in two dimensions
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Metadata
- Authors
- Douglas, M., & Nekrasov, N.
- Affiliations
- Rutgers, The State University of New Jersey (US)
- Institute for Theoretical and Experimental Physics (RU)
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 2001-11
- Volume
- 73
- Issue
- 4
- Pages
- 977-1029
- ISSN
- 0034-6861 (ISSN-L)
- 1539-0756
- OpenAlex
- W1974665356
- Semantic Scholar
- ff829c1cab7a67ce29a3e6216b9b516d6929750f
- Cited by
- 2,096
- References
- 289
- Citations by year
- 2026: 27 · 2025: 46 · 2024: 60 · 2023: 58 · 2022: 49 · 2021: 37 · 2020: 40 · 2019: 66 · 2018: 63 · 2017: 68 · 2016: 84 · 2015: 63 · 2014: 86 · 2013: 85 · 2012: 91
- FWCI
- 89.23
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Reviews of Modern Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- noncommutative field theory, noncommutative spacetime, M-theory, string theory, quantum Hall states, noncommutative geometry, classical field theory, quantum field theory
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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