Articles de revues : « Gauge theory on noncommutative spaces »

1

Madore, J., S. Schraml, P. Schupp et J. Wess. « Gauge theory on noncommutative spaces ». European Physical Journal C 16, n^o 1 (août 2000) : 161–67. http://dx.doi.org/10.1007/s100520050012.

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Manolakos, George, Pantelis Manousselis, Danai Roumelioti, Stelios Stefas et George Zoupanos. « A Matrix Model of Four-Dimensional Noncommutative Gravity ». Universe 8, n^o 4 (28 mars 2022) : 215. http://dx.doi.org/10.3390/universe8040215.

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In this review, we revisit our latest works regarding the description of the gravitational interaction on noncommutative spaces as matrix models. Specifically, inspired by the gauge-theoretic approach of (ordinary) gravity, we make use of the suggested methodology, modified appropriately for the noncommutative framework, of the well-established formulation of gauge theories on them. Making use of a covariant four-dimensional fuzzy space, we formulate the gauge theory with an extended gauge group due to noncommutativity. In turn, in order to decrease the amount of symmetry we employ a symmetry breaking and result with an action which describes a theory that is a minimal noncommutative extension of the original.

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3

DIMITRIJEVIĆ, MARIJA, et LARISA JONKE. « TWISTED SYMMETRY AND NONCOMMUTATIVE FIELD THEORY ». International Journal of Modern Physics : Conference Series 13 (janvier 2012) : 54–65. http://dx.doi.org/10.1142/s2010194512006733.

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Although the meaning of twisted symmetry is still not fully understood, the twist approach has its advantages in the construction of field theories on noncommutative spaces. We discuss these advantages on the example of κ-Minkowski space-time. We construct the noncommutative U(1) gauge field theory. Especially the action is written as an integral of a maximal form, thus solving the cyclicity problem of the integral in κ-Minkowski. Using the Seiberg-Witten map to relate noncommutative and commutative degrees of freedom the effective action with the first order corrections in the deformation parameter is obtained.

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Manolakos, George, Pantelis Manousselis et George Zoupanos. « Gauge Theories : From Kaluza–Klein to noncommutative gravity theories ». Symmetry 11, n^o 7 (2 juillet 2019) : 856. http://dx.doi.org/10.3390/sym11070856.

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First, the Coset Space Dimensional Reduction scheme and the best particle physics model so far resulting from it are reviewed. Then, a higher-dimensional theory in which the extra dimensions are fuzzy coset spaces is described and a dimensional reduction to four-dimensional theory is performed. Afterwards, another scheme including fuzzy extra dimensions is presented, but this time the starting theory is four-dimensional while the fuzzy extra dimensions are generated dynamically. The resulting theory and its particle content is discussed. Besides the particle physics models discussed above, gravity theories as gauge theories are reviewed and then, the whole methodology is modified in the case that the background spacetimes are noncommutative. For this reason, specific covariant fuzzy spaces are introduced and, eventually, the program is written for both the 3-d and 4-d cases.

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5

Besnard, F., et S. Farnsworth. « Particle models from special Jordan backgrounds and spectral triples ». Journal of Mathematical Physics 63, n^o 10 (1 octobre 2022) : 103505. http://dx.doi.org/10.1063/5.0107136.

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We put forward a definition for spectral triples and algebraic backgrounds based on Jordan coordinate algebras. We also propose natural and gauge-invariant bosonic configuration spaces of fluctuated Dirac operators and compute them for general, almost-associative, Jordan, coordinate algebras. We emphasize that the theory so obtained is not equivalent with usual associative noncommutative geometry, even when the coordinate algebra is the self-adjoint part of a C*-algebra. In particular, in the Jordan case, the gauge fields are always unimodular, thus curing a long-standing problem in noncommutative geometry.

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Cirio, Lucio S., Giovanni Landi et Richard J. Szabo. « Instantons and vortices on noncommutative toric varieties ». Reviews in Mathematical Physics 26, n^o 09 (octobre 2014) : 1430008. http://dx.doi.org/10.1142/s0129055x14300088.

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We elaborate on the quantization of toric varieties by combining techniques from toric geometry, isospectral deformations and noncommutative geometry in braided monoidal categories, and the construction of instantons thereon by combining methods from noncommutative algebraic geometry and a quantized twistor theory. We classify the real structures on a toric noncommutative deformation of the Klein quadric and use this to derive a new noncommutative four-sphere which is the unique deformation compatible with the noncommutative twistor correspondence. We extend the computation of equivariant instanton partition functions to noncommutative gauge theories with both adjoint and fundamental matter fields, finding agreement with the classical results in all instances. We construct moduli spaces of noncommutative vortices from the moduli of invariant instantons, and derive corresponding equivariant partition functions which also agree with those of the classical limit.

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7

CHAMSEDDINE, ALI H. « COMPLEX GRAVITY AND NONCOMMUTATIVE GEOMETRY ». International Journal of Modern Physics A 16, n^o 05 (20 février 2001) : 759–66. http://dx.doi.org/10.1142/s0217751x01003883.

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The presence of a constant background antisymmetric tensor for open strings or D-branes forces the space-time coordinates to be noncommutative. An immediate consequence of this is that all fields get complexified. By applying this idea to gravity one discovers that the metric becomes complex. Complex gravity is constructed by gauging the symmetry U(1, D-1). The resulting action gives one specific form of nonsymmetric gravity. In contrast to other theories of nonsymmetric gravity the action is both unique and gauge invariant. It is argued that for this theory to be consistent one must prove the existence of generalized diffeomorphism invariance. The results are easily generalized to noncommutative spaces.

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CASTRO, CARLOS. « THE CLIFFORD SPACE GEOMETRY OF CONFORMAL GRAVITY AND U(4) × U(4) YANG–MILLS UNIFICATION ». International Journal of Modern Physics A 25, n^o 01 (10 janvier 2010) : 123–43. http://dx.doi.org/10.1142/s0217751x1004752x.

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It is shown how a conformal gravity and U (4) × U (4) Yang–Mills grand unification model in four dimensions can be attained from a Clifford gauge field theory in C-spaces (Clifford spaces) based on the (complex) Clifford Cl (4, C) algebra underlying a complexified four-dimensional space–time (eight real dimensions). Upon taking a real slice, and after symmetry breaking, it leads to ordinary gravity and the Standard Model in four real dimensions. A brief conclusion about the noncommutative star-product deformations of this Grand Unified Theory of gravity with the other forces of Nature is presented.

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9

Morvan, Xavier. « A noncommutative generalization of Thurston’s gluing equations ». International Journal of Mathematics 28, n^o 12 (novembre 2017) : 1750089. http://dx.doi.org/10.1142/s0129167x17500896.

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In his famous Princeton Notes, Thurston introduced the so-called gluing equations defining the deformation variety. Later, Kashaev defined a noncommutative ring from H-triangulations of 3-manifolds and observed that for trefoil and figure-eight knot complements the abelianization of this ring is isomorphic to the ring of regular functions on the deformation variety, Kashaev, [Formula: see text]-groupoids in knot theory, Geom. Dedicata 150(1) (2010) 105–130; Kashaev, Noncommutative teichmüller spaces and deformation varieties of knot completeness; Kashaev, Delta-groupoids and ideal triangulation in Chern–Simons gauge theory: 20 Years After, AMS/IP Studies Advanced Mathematics, Vol. 50 (American Mathematical Society, RI, 2011). In this paper, we prove that this is true for any knot complement in a homology sphere. We also analyze some examples on other manifolds.

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10

LIZZI, FEDELE. « STRINGS, NONCOMMUTATIVE GEOMETRY AND THE SIZE OF THE TARGET SPACE ». International Journal of Modern Physics A 14, n^o 28 (10 novembre 1999) : 4501–17. http://dx.doi.org/10.1142/s0217751x99002116.

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We describe how the presence of the antisymmetric tensor (torsion) on the world sheet action of string theory renders the size of the target space a gauge noninvariant quantity. This generalizes the R ↔ 1/R symmetry in which momenta and windings are exchanged, to the whole O(d,d,ℤ). The crucial point is that, with a transformation, it is possible always to have all of the lowest eigenvalues of the Hamiltonian to be momentum modes. We interpret this in the framework of noncommutative geometry, in which algebras take the place of point spaces, and of the spectral action principle for which the eigenvalues of the Dirac operator are the fundamental objects, out of which the theory is constructed. A quantum observer, in the presence of many low energy eigenvalues of the Dirac operator (and hence of the Hamiltonian) will always interpreted the target space of the string theory as effectively uncompactified.

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11

BRACE, D., B. L. CERCHIAI et B. ZUMINO. « NONABELIAN GAUGE THEORIES ON NONCOMMUTATIVE SPACES ». International Journal of Modern Physics A 17, supp01 (octobre 2002) : 205–17. http://dx.doi.org/10.1142/s0217751x02013137.

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In this paper, we describe a method for obtaining the nonabelian Seiberg-Witten map for any gauge group and to any order in θ. The equations defining the Seiberg-Witten map are expressed using a coboundary operator, so that they can be solved by constructing a corresponding homotopy operator. The ambiguities, of both the gauge and covariant type, which arise in this map are manifest in our formalism.

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12

SZABO, RICHARD J. « DISCRETE NONCOMMUTATIVE GAUGE THEORY ». Modern Physics Letters A 16, n^o 04n06 (28 février 2001) : 367–86. http://dx.doi.org/10.1142/s0217732301003474.

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A review of the relationships between matrix models and noncommutative gauge theory is presented. A lattice version of noncommutative Yang–Mills theory is constructed and used to examine some generic properties of noncommutative quantum field theory, such as uv/ir mixing and the appearance of gauge-invariant open Wilson line operators. Morita equivalence in this class of models is derived and used to establish the generic relation between noncommutative gauge theory and twisted reduced models. Finite-dimensional representations of the quotient conditions for toroidal compactification of matrix models are thereby exhibited. The coupling of noncommutative gauge fields to fundamental matter fields is considered and a large mass expansion is used to study the properties of gauge-invariant observables. Morita equivalence with fundamental matter is also presented and used to prove the equivalence between the planar loop renormalizations in commutative and noncommutative quantum chromodynamics.

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13

de Goursac, A., J. C. Wallet et R. Wulkenhaar. « Noncommutative induced gauge theory ». European Physical Journal C 51, n^o 4 (août 2007) : 977–87. http://dx.doi.org/10.1140/epjc/s10052-007-0335-2.

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14

Rozali, Moshe, et Mark Van Raamsdonk. « Gauge invariant correlators in noncommutative gauge theory ». Nuclear Physics B 608, n^o 1-2 (août 2001) : 103–24. http://dx.doi.org/10.1016/s0550-3213(01)00257-7.

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15

Wallet, J.-C. « Noncommutative induced gauge theories on Moyal spaces ». Journal of Physics : Conference Series 103 (1 février 2008) : 012007. http://dx.doi.org/10.1088/1742-6596/103/1/012007.

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16

Jurčo, Branislav, Peter Schupp et Julius Wess. « Nonabelian noncommutative gauge theory via noncommutative extra dimensions ». Nuclear Physics B 604, n^o 1-2 (juin 2001) : 148–80. http://dx.doi.org/10.1016/s0550-3213(01)00191-2.

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17

Gross, David J., et Nikita A. Nekrasov. « Solitons in noncommutative gauge theory ». Journal of High Energy Physics 2001, n^o 03 (28 mars 2001) : 044. http://dx.doi.org/10.1088/1126-6708/2001/03/044.

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18

MENDES, A. C. R., C. NEVES, W. OLIVEIRA et F. I. TAKAKURA. « NONCOMMUTATIVE METAFLUID DYNAMICS ». International Journal of Modern Physics A 21, n^o 03 (30 janvier 2006) : 505–16. http://dx.doi.org/10.1142/s0217751x06028862.

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In this paper we define a noncommutative (NC) metafluid dynamics.1,2 We applied the Dirac's quantization to the metafluid dynamics on NC spaces. First class constraints were found which are the same obtained in Ref. 4. The gauge covariant quantization of the nonlinear equations of fields on noncommutative spaces were studied. We have found the extended Hamiltonian which leads to equations of motion in the gauge covariant form. In addition, we show that a particular transformation3 on the usual classical phase space (CPS) leads to the same results as of the ⋆-deformation with ν = 0. Besides, we have shown that an additional term is introduced into the dissipative force due to the NC geometry. This is an interesting feature due to the NC nature induced into model.

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19

Matsubara, Keizo. « Restrictions on gauge groups in noncommutative gauge theory ». Physics Letters B 482, n^o 4 (juin 2000) : 417–19. http://dx.doi.org/10.1016/s0370-2693(00)00549-9.

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20

SCHRAML, STEFAN. « ENVELOPING ALGEBRA-VALUED GAUGE TRANSFORMATIONS ON NONCOMMUTATIVE SPACES ». Modern Physics Letters A 16, n^o 04n06 (28 février 2001) : 337–41. http://dx.doi.org/10.1142/s0217732301003437.

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21

AGARWAL, A., et L. AKANT. « GAUGE THEORIES ON OPEN LIE ALGEBRA NONCOMMUTATIVE SPACES ». Modern Physics Letters A 18, n^o 07 (7 mars 2003) : 491–501. http://dx.doi.org/10.1142/s0217732303009587.

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It is shown that noncommutative spaces, which are quotients of associative algebras by ideals generated by highly nonlinear relations of a particular type, admit extremely simple formulae for deformed or star products. Explicit construction of these star products is carried out. Quantum gauge theories are formulated on these spaces, and the Seiberg–Witten map is worked out in detail.

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22

PAL, SHESANSU SEKHAR. « A NOTE ON NONCOMMUTATIVE STRING THEORY AND ITS LOW ENERGY LIMIT ». International Journal of Modern Physics A 18, n^o 10 (20 avril 2003) : 1733–47. http://dx.doi.org/10.1142/s0217751x03014162.

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The noncommutative string theory is described by embedding open string theory in a constant second rank antisymmetric Bμν field and the noncommutative gauge theory is defined by a deformed ⋆ product. As a check, the study of various scattering amplitudes in both noncommutative string and noncommutative gauge theory confirms that in the α′ → 0 limit, the noncommutative string theoretic amplitude goes over to the noncommutative gauge theoretic amplitude and the couplings are related as [Formula: see text]. Furthermore, we show that in this limit there will not be any correction to the gauge theoretic action because of the absence of massive modes. We get sin/cos factors in the scattering amplitudes depending on the odd/even number of external photons.

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23

Kauffman, Louis H. « Calculus, Gauge Theory and Noncommutative Worlds ». Symmetry 14, n^o 3 (22 février 2022) : 430. http://dx.doi.org/10.3390/sym14030430.

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This paper shows how gauge theoretic structures arise in a noncommutative calculus where the derivations are generated by commutators. These patterns include Hamilton’s equations, the structure of the Levi–Civita connection, and generalizations of electromagnetism that are related to gauge theory and with the early work of Hermann Weyl. The territory here explored is self-contained mathematically. It is elementary, algebraic, and subject to possible generalizations that are discussed in the body of the paper.

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24

Lechtenfeld, Olaf, Alexander D. Popov et Richard J. Szabo. « Quiver Gauge Theory and Noncommutative Vortices ». Progress of Theoretical Physics Supplement 171 (2007) : 258–68. http://dx.doi.org/10.1143/ptps.171.258.

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25

Gopakumar, Rajesh, Juan Maldacena, Shiraz Minwalla et Andrew Strominger. « S-duality and noncommutative gauge theory ». Journal of High Energy Physics 2000, n^o 06 (23 juin 2000) : 036. http://dx.doi.org/10.1088/1126-6708/2000/06/036.

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Bergman, Aaron, et Ori J. Ganor. « Dipoles, twists and noncommutative gauge theory ». Journal of High Energy Physics 2000, n^o 10 (9 octobre 2000) : 018. http://dx.doi.org/10.1088/1126-6708/2000/10/018.

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Aganagic, Mina, Rajesh Gopakumar, Shiraz Minwalla et Andrew Strominger. « Unstable solitons in noncommutative gauge theory ». Journal of High Energy Physics 2001, n^o 04 (1 avril 2001) : 001. http://dx.doi.org/10.1088/1126-6708/2001/04/001.

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28

Steinacker, Harold. « Emergent gravity from noncommutative gauge theory ». Journal of High Energy Physics 2007, n^o 12 (12 décembre 2007) : 049. http://dx.doi.org/10.1088/1126-6708/2007/12/049.

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29

Popović, D. S., et B. Sazdović. « Canonical approach to noncommutative gauge theory ». Physics Letters B 683, n^o 4-5 (janvier 2010) : 349–53. http://dx.doi.org/10.1016/j.physletb.2009.12.027.

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Jurčo, Branislav, Peter Schupp et Julius Wess. « Noncommutative gauge theory for Poisson manifolds ». Nuclear Physics B 584, n^o 3 (septembre 2000) : 784–94. http://dx.doi.org/10.1016/s0550-3213(00)00363-1.

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31

Kraus, Per, Arvind Rajaraman et Stephen Shenker. « Tachyon condensation in noncommutative gauge theory ». Nuclear Physics B 598, n^o 1-2 (mars 2001) : 169–88. http://dx.doi.org/10.1016/s0550-3213(00)00733-1.

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32

Horváthy, P. A., et P. C. Stichel. « Moving vortices in noncommutative gauge theory ». Physics Letters B 583, n^o 3-4 (mars 2004) : 353–56. http://dx.doi.org/10.1016/j.physletb.2003.12.063.

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33

Ambjørn, J., Y. M. Makeenko, J. Nishimura et R. J. Szabo. « Nonperturbative dynamics of noncommutative gauge theory ». Physics Letters B 480, n^o 3-4 (mai 2000) : 399–408. http://dx.doi.org/10.1016/s0370-2693(00)00391-9.

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34

Kurkov, Maxim, et Patrizia Vitale. « The Gribov problem in noncommutative gauge theory ». International Journal of Geometric Methods in Modern Physics 15, n^o 07 (24 mai 2018) : 1850119. http://dx.doi.org/10.1142/s0219887818501190.

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After reviewing Gribov ambiguity of non-Abelian gauge theories, a phenomenon related to the topology of the bundle of gauge connections, we show that there is a similar feature for noncommutative QED over Moyal space, despite the structure group being Abelian, and we exhibit an infinite number of solutions for the equation of Gribov copies. This is a genuine effect of noncommutative geometry which disappears when the noncommutative parameter vanishes.

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35

Vacaru, Sergiu I. « Gauge and Einstein gravity from non-abelian gauge models on noncommutative spaces ». Physics Letters B 498, n^o 1-2 (janvier 2001) : 74–82. http://dx.doi.org/10.1016/s0370-2693(00)01369-1.

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36

Jurčo, B., L. Möller, S. Schraml, P. Schupp et J. Wess. « Construction of non-Abelian gauge theories on noncommutative spaces ». European Physical Journal C 21, n^o 2 (juin 2001) : 383–88. http://dx.doi.org/10.1007/s100520100731.

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37

Liang, Shi-Dong. « Klein-Gordon Theory in Noncommutative Phase Space ». Symmetry 15, n^o 2 (30 janvier 2023) : 367. http://dx.doi.org/10.3390/sym15020367.

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We extend the three-dimensional noncommutative relations of the position and momentum operators to those in the four dimension. Using the Seiberg-Witten (SW) map, we give the Heisenberg representation of these noncommutative algebras and endow the noncommutative parameters associated with the Planck constant, Planck length and cosmological constant. As an analog with the electromagnetic gauge potential, the noncommutative effect can be interpreted as an effective gauge field, which depends on the Plank constant and cosmological constant. Based on these noncommutative relations, we give the Klein-Gordon (KG) equation and its corresponding current continuity equation in the noncommutative phase space including the canonical and Hamiltonian forms and their novel properties beyond the conventional KG equation. We analyze the symmetries of the KG equations and some observables such as velocity and force of free particles in the noncommutative phase space. We give the perturbation solution of the KG equation.

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38

ZET, G. « U(2) GAUGE THEORY ON NONCOMMUTATIVE GEOMETRY ». International Journal of Modern Physics A 24, n^o 15 (20 juin 2009) : 2889–97. http://dx.doi.org/10.1142/s0217751x09046230.

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We develop a model of gauge theory with U (2) as local symmetry group over a noncommutative space-time. The integral of the action is written considering a gauge field coupled with a Higgs multiplet. The gauge fields are calculated up to the second order in the noncommutativity parameter using the equations of motion and Seiberg-Witten map. The solutions are determined order by order supposing that in zeroth-order they have a general relativistic analog form. The Wu-Yang ansatz for the gauge fields is used to solve the field equations. Some comments on the quantization of the electrical and magnetical charges are also given, with a comparison between commutative and noncommutative cases.

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39

Ćaćić, Branimir, et Bram Mesland. « Gauge Theory on Noncommutative Riemannian Principal Bundles ». Communications in Mathematical Physics 388, n^o 1 (11 octobre 2021) : 107–98. http://dx.doi.org/10.1007/s00220-021-04187-8.

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Grosse, H., et M. Wohlgenannt. « Induced gauge theory on a noncommutative space ». European Physical Journal C 52, n^o 2 (31 juillet 2007) : 435–50. http://dx.doi.org/10.1140/epjc/s10052-007-0369-5.

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UPADHYAY, SUDHAKER, et BHABANI PRASAD MANDAL. « NONCOMMUTATIVE GAUGE THEORIES : MODEL FOR HODGE THEORY ». International Journal of Modern Physics A 28, n^o 25 (8 octobre 2013) : 1350122. http://dx.doi.org/10.1142/s0217751x13501224.

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The nilpotent Becchi–Rouet–Stora–Tyutin (BRST), anti-BRST, dual-BRST and anti-dual-BRST symmetry transformations are constructed in the context of noncommutative (NC) 1-form as well as 2-form gauge theories. The corresponding Noether's charges for these symmetries on the Moyal plane are shown to satisfy the same algebra, as by the de Rham cohomological operators of differential geometry. The Hodge decomposition theorem on compact manifold is also studied. We show that noncommutative gauge theories are field theoretic models for Hodge theory.

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Rajaraman, Arvind, et Moshe Rozali. « Noncommutative gauge theory, divergences and closed strings ». Journal of High Energy Physics 2000, n^o 04 (27 avril 2000) : 033. http://dx.doi.org/10.1088/1126-6708/2000/04/033.

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Gross, David J., et Nikita A. Nekrasov. « Monopoles and strings in noncommutative gauge theory ». Journal of High Energy Physics 2000, n^o 07 (20 juillet 2000) : 034. http://dx.doi.org/10.1088/1126-6708/2000/07/034.

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Gross, David J., et Nikita A. Nekrasov. « Dynamics of strings in noncommutative gauge theory ». Journal of High Energy Physics 2000, n^o 10 (11 octobre 2000) : 021. http://dx.doi.org/10.1088/1126-6708/2000/10/021.

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45

Dimakis, A., F. Muller-Hoissen et T. Striker. « Noncommutative differential calculus and lattice gauge theory ». Journal of Physics A : Mathematical and General 26, n^o 8 (21 avril 1993) : 1927–49. http://dx.doi.org/10.1088/0305-4470/26/8/019.

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46

Wohlgenannt, M. « Induced gauge theory on a noncommutative space ». Journal of Physics : Conference Series 103 (1 février 2008) : 012008. http://dx.doi.org/10.1088/1742-6596/103/1/012008.

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47

Horváthy, P. A., L. Martina et P. C. Stichel. « Galilean noncommutative gauge theory : symmetries and vortices ». Nuclear Physics B 673, n^o 1-2 (novembre 2003) : 301–18. http://dx.doi.org/10.1016/j.nuclphysb.2003.09.027.

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48

Göckeler, Meinulf, et Thomas Schücker. « Does noncommutative geometry encompass lattice gauge theory ? » Physics Letters B 434, n^o 1-2 (août 1998) : 80–82. http://dx.doi.org/10.1016/s0370-2693(98)00734-5.

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Demidov, S. V., S. L. Dubovsky, V. A. Rubakov et S. M. Sibiryakov. « Gauge Theory Solitons on the Noncommutative Cylinder ». Theoretical and Mathematical Physics 138, n^o 2 (février 2004) : 269–83. http://dx.doi.org/10.1023/b:tamp.0000015073.02483.03.

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Wohlgenannt, M. « Induced gauge theory on a noncommutative space ». Fortschritte der Physik 56, n^o 4-5 (18 avril 2008) : 547–51. http://dx.doi.org/10.1002/prop.200710533.

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