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The aim of this review is to present an overview over available models and approaches to non-commutative gauge theory.
1914
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Schrödinger E., Über die Unanwendbarkeit der Geometrie im Kleinen,
1934
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Heisenberg W., Über die in der Theorie der Elementarteilchen auftretende universelle Länge,
1938
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Groenewold H.J., On the principles of elementary quantum mechanics,
1946
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Snyder H.S., Quantized space-time,
1947
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Snyder H.S., The electromagnetic field in quantized space-time,
1947
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Moyal J.E., Quantum mechanics as a statistical theory,
1949
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Landau L.D., On the quantum theory of fields, in Niels Bohr and the Development of Physics, McGraw-Hill Book Co., New York, N.Y., 1955, 52–69
1955
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Gribov V.N., Quantization of non-Abelian gauge theories,
1978
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Batalin I.A., Vilkovisky G.A., Gauge algebra and quantization,
1981
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Batalin I.A., Vilkovisky G.A., Quantization of gauge theories with linearly dependent generators,
1983
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Zwanziger D., Local and renormalizable action from the Gribov horizon,
1989
Earlier work this paper cites.
Reshetikhin N., Takhtadzhyan L., Faddeev L., Quantization of Lie groups and Lie algebras,
1990
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Madore J., The commutative limit of a matrix geometry,
1991
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Lukierski J., Ruegg H., Nowicki A., Tolstoi V.N.,
1991
Earlier work this paper cites.
Rivasseau V., From perturbative to constructive renormalization,
1991
Earlier work this paper cites.
Madore J., The fuzzy sphere,
1992
Earlier work this paper cites.
Zwanziger D., Renormalizability of the critical limit of lattice gauge theory by BRS invariance,
1993
Earlier work this paper cites.
Connes A., Noncommutative geometry, Academic Press, Inc., San Diego, CA, 1994
1994
Earlier work this paper cites.
Majid S., Ruegg H., Bicrossproduct structure of
1994
Earlier work this paper cites.
Doplicher S., Fredenhagen K., Roberts J.E., The quantum structure of spacetime at the Planck scale and quantum fields,
1995
Earlier work this paper cites.
Piguet O., Sorella S.P., Algebraic renormalization. Perturbative renormalization, symmetries and anomalies,
1995
Earlier work this paper cites.
Filk T., Divergencies in a field theory on quantum space,
1996
Earlier work this paper cites.
Ryder L.H., Quantum field theory, 2nd ed., Cambridge University Press, Cambridge, 1996
1996
Earlier work this paper cites.
Boulatov D.V., Quantum deformation of lattice gauge theory,
1997
Earlier work this paper cites.
Ishibashi N., Kawai H., Kitazawa Y., Tsuchiya A., A large-
1997
Earlier work this paper cites.
Klimčík C., Gauge theories on the noncommutative sphere,
1998
Earlier work this paper cites.
Emery S., Krüger M., Rant J., Schweda M., Sommer T., Two-dimensional BF model quantized in the axial gauge,
1998
Earlier work this paper cites.
Del Cima O.M., Landsteiner K., Schweda M., Twisted
1998
Earlier work this paper cites.
Boresch A., Emery S., Moritsch O., Schweda M., Sommer T., Zerrouki H., Applications of noncovariant gauges in the algebraic renormalization procedure, World Scientific Publishing Co., Inc., River Edge, NJ, 1998
1998
Earlier work this paper cites.
Seiberg N., Witten E., String theory and noncommutative geometry,
1999
Earlier work this paper cites.
Majid S., Diagrammatics of braided group gauge theory,
1999
Earlier work this paper cites.
Sheikh-Jabbari M.M., One loop renormalizability of supersymmetric Yang-Mills theories on noncommutative two-torus,
1999
Earlier work this paper cites.
Landi G., Lizzi F., Szabo R.J., String geometry and the noncommutative torus,
1999
Earlier work this paper cites.
Del Cima O.M., Grimstrup J.M., Schweda M., On the finiteness of a new topological model in
1999
Earlier work this paper cites.
Madore J., An introduction to noncommutative differential geometry and its physical applications, 2nd ed.,
1999
Earlier work this paper cites.
Kulish P.P., Mudrov A.I., Twist-related geometries on
1999
Earlier work this paper cites.
Minwalla S., Van Raamsdonk M., Seiberg N., Noncommutative perturbative dynamics,
2000
Earlier work this paper cites.
Matusis A., Susskind L., Toumbas N., The IR/UV connection in the non-commutative gauge theories,
2000
Earlier work this paper cites.
Girotti H.O., Gomes M., Rivelles V.O., da Silva A.J., A consistent noncommutative field theory: the Wess–Zumino model,
2000
Earlier work this paper cites.
Bichl A.A., Grimstrup J., Grosse H., Popp L., Schweda M., Wulkenhaar R., The superfield formalism applied to the noncommutative Wess–Zumino model,
2000
Earlier work this paper cites.
Ferrara S., Lledó M.A., Some aspects of deformations of supersymmetric field theories,
2000
Earlier work this paper cites.
Terashima S., A note on superfields and noncommutative geometry,
2000
Earlier work this paper cites.
Matsubara K., Restrictions on gauge groups in noncommutative gauge theory,
2000
Earlier work this paper cites.
Hayakawa M., Perturbative analysis on infrared aspects of noncommutative QED on
2000
Earlier work this paper cites.
Krajewski T., Wulkenhaar R., Perturbative quantum gauge fields on the noncommutative torus,
2000
Earlier work this paper cites.
Jurčo B., Schupp P., Wess J., Noncommutative gauge theory for Poisson manifolds,
2000
Earlier work this paper cites.
Gieres F., Grimstrup J.M., Pisar T., Schweda M., Vector supersymmetry in topological field theories,
2000
Earlier work this paper cites.
Oeckl R., Untwisting noncommutative
2000
Earlier work this paper cites.
Majid S., Quantum groups and noncommutative geometry,
2000
Earlier work this paper cites.
Chepelev I., Roiban R., Convergence theorem for non-commutative Feynman graphs and renormalization,
2001
Earlier work this paper cites.
Jurčo B., Möller L., Schraml S., Schupp P., Wess J., Construction of non-Abelian gauge theories on noncommutative spaces,
2001
Earlier work this paper cites.
Bichl A.A., Grimstrup J.M., Grosse H., Popp L., Schweda M., Wulkenhaar R., Renormalization of the noncommutative photon self-energy to all orders via Seiberg–Witten map,
2001
Earlier work this paper cites.
Balachandran A.P., Vaidya S., Instantons and chiral anomaly in fuzzy physics,
2001
Earlier work this paper cites.
Iso S., Kimura Y., Tanaka K., Wakatsuki K., Noncommutative gauge theory on fuzzy sphere from matrix model,
2001
Earlier work this paper cites.
Jack I., Jones D.R.T., Ultra-violet finiteness in noncommutative supersymmetric theories,
2001
Earlier work this paper cites.
Aref’eva I.Y., Belov D.M., Koshelev A.S., Rytchkov O.A., UV/IR mixing for noncommutative complex scalar field theory interacting with gauge fields,
2001
Earlier work this paper cites.
Micu A., Sheikh Jabbari M.M., Noncommutative
2001
Earlier work this paper cites.
Martín C.P., Sánchez-Ruiz D., The BRS invariance of noncommutative
2001
Earlier work this paper cites.
Liao Y., One loop renormalization of spontaneously broken U(2) gauge theory on noncommutative spacetime,
2001
Earlier work this paper cites.
Ruiz Ruiz F., Gauge-fixing independence of IR divergences in non-commutative U(1), perturbative tachyonic instabilities and supersymmetry,
2001
Earlier work this paper cites.
Van Raamsdonk M., The meaning of infrared singularities in noncommutative gauge theories,
2001
Earlier work this paper cites.
Armoni A., Comments on perturbative dynamics of non-commutative Yang–Mills theory,
2001
Earlier work this paper cites.
Martín C.P., Ruiz Ruiz F., Paramagnetic dominance, the sign of the beta function and UV/IR mixing in non-commutative U(1),
2001
Earlier work this paper cites.
Landi G., Lizzi F., Szabo R.J., From large
2001
Earlier work this paper cites.
Hewett J.L., Petriello F.J., Rizzo T.G., Signals for non-commutative interactions at linear colliders,
2001
Earlier work this paper cites.
Carlson C.E., Carone C.D., Lebed R.F., Bounding noncommutative QCD,
2001
Cited alongside, same era.
Denk S., Perturbative aspects of non-local and non-commutative quantum field theories, PhD Thesis, Vienna University of Technology, 2004, available at
2001
Cited alongside, same era.
Langmann E., Szabo R.J., Duality in scalar field theory on noncommutative phase spaces,
2002
Cited alongside, same era.
Calmet X., Jurčo B., Schupp P., Wess J., Wohlgenannt M., The standard model on non-commutative space-time,
2002
Cited alongside, same era.
Burić M., Radovanović V., The one-loop effective action for quantum electrodynamics on noncommutative space,
2002
Cited alongside, same era.
Wulkenhaar R., Non-renormalizability of
Carone C.D., Phenomenology of noncommutative field theories,
2006
Later among the works it cites.
Rivasseau V., Vignes-Tourneret F., Wulkenhaar R., Renormalization of noncommutative
2006
Later among the works it cites.
Aschieri P., Dimitrijević M., Meyer F., Schraml S., Wess J., Twisted gauge theories,
2006
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Vassilevich D.V., Twist to close,
2006
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Barrett J.W., Lorentzian version of the noncommutative geometry of the Standard Model of particle physics,
2007
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de Goursac A., Wallet J.-C., Wulkenhaar R., Noncommutative induced gauge theory,
2007
Later among the works it cites.
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2002
Cited alongside, same era.
Trampetić J., Rare and forbidden decays,
2002
Cited alongside, same era.
Karabali D., Nair V.P., Polychronakos A.P., Spectrum of Schrödinger field in a noncommutative magnetic monopole,
2002
Cited alongside, same era.
Alexanian G., Balachandran A.P., Immirzi G., Ydri B., Fuzzy
2002
Cited alongside, same era.
Chaichian M., Prešnajder P., Sheikh-Jabbari M.M., Tureanu A., Noncommutative gauge field theories: a no-go theorem,
2002
Cited alongside, same era.
Armoni A., Lopez E., UV/IR mixing via closed strings and tachyonic instabilities,
2002
Cited alongside, same era.
Carlson C.E., Carone C.D., Zobin N., Noncommutative gauge theory without Lorentz violation,
2002
Cited alongside, same era.
2007
Later among the works it cites.
Burić M., Radovanović V., Trampetić J., The one-loop renormalization of the gauge sector in the
2007
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Burić M., Latas D., Radovanović V., Trampetić J., Nonzero
2007
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Blaschke D.N., Hohenegger S., A generalization of Slavnov-extended non-commutative gauge theories,
2007
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Steinacker H., Emergent gravity from noncommutative gauge theory,
2007
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2007
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Alboteanuv A., Ohl T., Ruckl R., The noncommutative standard model at
2007
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Trampetic J., Wohlgenannt M., Comment on the 2nd order Seiberg–Witten maps,
2007
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Martín C.P., Sánchez-Ruiz D., Tamarit C., The noncommutative U(1) Higgs–Kibble model in the enveloping-algebra formalism and its renormalizability,
2007
Later among the works it cites.
Latas D., Radovanović V., Trampetić J., Non-commutative
2007
Later among the works it cites.
Disertori M., Rivasseau V., Two- and three-loop beta function of non-commutative
2007
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Disertori M., Gurau R., Magnen J., Rivasseau V., Vanishing of beta function of non-commutative
2007
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Banerjee R., Samanta S., Gauge generators, transformations and identities on a noncommutative space,
2007
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2007
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Grosse H., Lechner G., Noncommutative deformations of Wightman quantum field theories,
2008
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Magnen J., Rivasseau V., Constructive
2008
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Wohlgenannt M., Induced gauge theory on a noncommutative space,
2008
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2008
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Schupp P., You J., UV/IR mixing in noncommutative QED defined by Seiberg–Witten map,
2008
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Grosse H., Steinacker H., Wohlgenannt M., Emergent gravity, matrix models and UV/IR mixing,
2008
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Klammer D., Steinacker H., Fermions and emergent noncommutative gravity,
2008
Later among the works it cites.
Gitman D.M., Vassilevich D.V., Space-time noncommutativity with a bifermionic parameter,
2008
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Burić M., Latas D., Radovanović V., Trampetić J., Absence of the 4
2008
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2008
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2008
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Akofor E., Balachandran A.P., Joseph A., Quantum fields on the Groenewold–Moyal plane,
2008
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Meljanac S., Samsarov A., Stojić M., Gupta K.S.,
2008
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2009
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2009
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2009
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2009
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Tamarit C., Trampetić J., Noncommutative fermions and quarkonia decays,
2009
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2009
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Horvat R., Trampetić J., Constraining spacetime noncommutativity with primordial nucleosynthesis,
2009
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Bolokhov P.A., Pospelov M., Low-energy constraints on
2009
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Martín C.P., Tamarit C., Noncommutative
2009
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Yang H.S., Instantons and emergent geometry,
2009
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2009
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2009
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Fischer A., Szabo R.J., Duality covariant quantum field theory on noncommutative Minkowski space,
2009
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Grumiller D., Rebhan A., Vassilevich D. (Editors), Fundamental interactions – a memorial volume for Wolfgang Kummer, World Scientific, Singapore, 2009
2009
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2009
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Sedmik R.I.P., On the development of non-commutative translation-invariant quantum gauge field models, PhD Thesis, Vienna University of Technology, 2009, available at
2009
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Rofner A., Investigations on the renormalizability of a non-commutative
2009
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Wess J., Deformed gauge theories, in Noncommutative Spacetimes,
2009
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Chaichian M., Tureanu A., Zet G., Gauge field theories with covariant star-product,
2009
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Vassilevich D.V., Diffeomorphism covariant star products and noncommutative gravity,
2009
Later among the works it cites.
2010
Closest in time.
Buric M., Grosse H., Madore J., Gauge fields on noncommutative geometries with curvature,
2010
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Buric M., Wohlgenannt M., Geometry of the Grosse–Wulkenhaar model,
2010
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2010
Closest in time.
Raasakka M., Tureanu A., On UV/IR mixing via Seiberg–Witten map for noncommutative QED,
2010
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Harikumar E., Maxwell’s equations on the
2010
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2010
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2010
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2010
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Steinacker H., Emergent geometry and gravity from matrix models: an introduction,
2010
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2010
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Steinacker H., Emergent gravity and noncommutative branes from Yang–Mills matrix models,
2032
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Freidel L., Livine E.R., Ponzano–Regge model revisited. III. Feynman diagrams and effective field theory,
2061
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