Author
Branislav Jurco
Other affiliations: CERN, Ludwig Maximilian University of Munich, Max Planck Society
Bio: Branislav Jurco is an academic researcher from Charles University in Prague. The author has contributed to research in topics: Gauge theory & Noncommutative geometry. The author has an hindex of 26, co-authored 65 publications receiving 3272 citations. Previous affiliations of Branislav Jurco include CERN & Ludwig Maximilian University of Munich.
Papers published on a yearly basis
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TL;DR: In this paper, a non-Abelian gauge theory on non-commutative spaces (induced via a star product with a constant Poisson tensor) is constructed from a consistency relation.
Abstract: We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories.
377 citations
TL;DR: In this article, the standard model on a non-commutative space was considered and the action in the noncommutativity parameter was extended to include the leading order action, and the most striking features were couplings between quarks, gluons and electroweak bosons and new vertices in the charged and neutral currents.
Abstract: We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter $\theta^{\mu
u}$
. No new particles are introduced; the structure group is $SU(3)\times SU(2)\times U(1)$
. We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in $\theta^{\mu
u}$
we find new vertices which are absent in the standard model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered.
329 citations
TL;DR: In this paper, an enveloping algebra-valued gauge field is constructed with the Seiberg-Witten map, which allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces.
Abstract: An enveloping algebra-valued gauge field is constructed, its components are functions of the Lie algebra-valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces.
328 citations
TL;DR: In this paper, the authors construct non-Abelian gauge theories on non-commutative spaces (induced via a star product with aconstant Poisson tensor) from a consistency relation.
Abstract: We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with aconstant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories.
285 citations
TL;DR: In this paper, the equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and non-commutative gauge theory (Seiberg-Witten map).
200 citations
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TL;DR: The generalization of field theory to space-time with noncommuting coordinates has been studied intensively in the last few years and many qualitatively new phenomena have been discovered, on both the classical and quantum level as discussed by the authors.
Abstract: 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.
2,306 citations
TL;DR: In this article, a pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity.
1,752 citations
TL;DR: Baxter has inherited the mantle of Onsager who started the process by solving exactly the two-dimensional Ising model in 1944 as mentioned in this paper, and there has been a growing belief that all the twodimensional lattice statistical models will eventually be solved and that it will be Professor Baxter who solves them.
Abstract: R J Baxter 1982 London: Academic xii + 486 pp price £43.60 Over the past few years there has been a growing belief that all the twodimensional lattice statistical models will eventually be solved and that it will be Professor Baxter who solves them. Baxter has inherited the mantle of Onsager who started the process by solving exactly the two-dimensional Ising model in 1944.
1,658 citations
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TL;DR: A model of Euclidean spacetime is presented in which at scales less than a certain length kappa the notion of a point does not exist and the algebra which determines the structure of the model is an algebra of matrices.
Abstract: A model of Euclidean spacetime is presented in which at scales less than a certain length kappa the notion of a point does not exist. At scales larger then kappa the model resembles the 2-sphere S2. The algebra which determines the structure of the model, and which replaces the algebra of functions, is an algebra of matrices. The order of n of the matrices is connected with the length kappa and the radius r of the sphere by the relation kappa approximately r/n. The elements of differential calculus are sketched as well as the possible definitions of a metric and linear connection. A definition of the path integral is given and a few examples of field theory on a fuzzy sphere are finally referred to.
903 citations