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Noncommutative Renormalization
 SÉMINAIRE POINCARÉ X (2007) 1 – 81
, 2007
"... A new version of scale analysis and renormalization theory has been found on the noncommutative Moyal space. It could be useful for physics beyond the standard model or for standard physics in strong external field. The good news is that quantum field theory is better behaved on noncommutative tha ..."
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Cited by 160 (29 self)
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A new version of scale analysis and renormalization theory has been found on the noncommutative Moyal space. It could be useful for physics beyond the standard model or for standard physics in strong external field. The good news is that quantum field theory is better behaved on noncommutative than on ordinary space: indeed it has no Landau ghost. Noncommutativity might therefore be an alternative to supersymmetry. We review this rapidly growing subject.
The multivariate Tutte polynomial (alias Potts model) for graphs and matroids, Surveys
, 2005
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Covariant Theory of Asymptotic Symmetries, Conservation Laws and Central Charges
, 2001
"... Under suitable assumptions on the boundary conditions, it is shown that there is a bijective correspondence between non trivial asymptotic reducibility parameters and non trivial asymptotically conserved n 2 forms in the context of Lagrangian gauge theories. The asymptotic reducibility parameters ar ..."
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Cited by 132 (17 self)
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Under suitable assumptions on the boundary conditions, it is shown that there is a bijective correspondence between non trivial asymptotic reducibility parameters and non trivial asymptotically conserved n 2 forms in the context of Lagrangian gauge theories. The asymptotic reducibility parameters are the parameters of gauge transformations that vanish suciently fast when evaluated at the background. A universal formula for asymptotically conserved n 2 forms in terms of the reducibility parameters is derived. Sucient conditions for niteness of the charges built out of the asymptotically conserved n 2 forms and for the existence of a Lie algebra g among equivalence classes of asymptotic reducibility parameters are given. The representation of g in terms of the charges may be centrally extended. An explicit and covariant formula for the central charges is constructed. They are shown to be 2cocycles on the Lie algebra g. The general considerations and formulas are applied to electrodynamics, YangMills theory and Einstein gravity where they reproduce familiar results.
Local BRST cohomology in the antifield formalism. I. General theorems
 COMM. MATH. PHYS
, 1995
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Moyal planes are spectral triples
, 2003
"... Axioms for nonunital spectral triples, extending those introduced in the unital case by Connes, are proposed. As a guide, and for the sake of their importance in noncommutative quantum field theory, the spaces R 2N endowed with Moyal products are intensively investigated. Some physical applications, ..."
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Cited by 75 (20 self)
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Axioms for nonunital spectral triples, extending those introduced in the unital case by Connes, are proposed. As a guide, and for the sake of their importance in noncommutative quantum field theory, the spaces R 2N endowed with Moyal products are intensively investigated. Some physical applications, such as the construction of noncommutative Wick monomials and the computation of the Connes–Lott functional action, are given for these noncommutative hyperplanes.
Statistical Mechanics: Entropy, Order Parameters, and Complexity
 Oxford Master Series in Physic
, 2006
"... The author provides this version of this manuscript with the primary intention of making the text accessible electronically—through web searches and for browsing and study on computers. Oxford University Press retains ownership of the copyright. Hardcopy printing, in particular, is subject to the s ..."
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Cited by 64 (2 self)
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The author provides this version of this manuscript with the primary intention of making the text accessible electronically—through web searches and for browsing and study on computers. Oxford University Press retains ownership of the copyright. Hardcopy printing, in particular, is subject to the same copyright rules as they would be for a printed book. CLARENDON PRESS. OXFORD
Consistent interactions between gauge fields: the cohomological approach
 In Henneaux et al. [54
"... Recent results on the cohomological reformulation of the problem of consistent interactions between gauge fields are illustrated in the case of the YangMills models. By evaluating the local BRST cohomology through descent equation techniques, it is shown (i) that there is a unique local, Poincaré i ..."
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Cited by 57 (3 self)
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Recent results on the cohomological reformulation of the problem of consistent interactions between gauge fields are illustrated in the case of the YangMills models. By evaluating the local BRST cohomology through descent equation techniques, it is shown (i) that there is a unique local, Poincaré invariant cubic vertex for free gauge vector fields which preserves the number of gauge symmetries to first order in the coupling constant; and (ii) that consistency to second order in the coupling constant requires the structure constants appearing in the cubic vertex to fulfill the Jacobi identity. The known uniqueness of the YangMills coupling is therefore rederived through cohomological arguments. 1.
Critical phenomena and renormalizationgroup theory
, 2008
"... We review results concerning the critical behavior of spin systems at equilibrium. We consider the Ising and the general O(N)symmetric universality class. For each of them, we review the estimates of the critical exponents, of the equation of state, of several amplitude ratios, and of the twopoint ..."
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Cited by 56 (12 self)
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We review results concerning the critical behavior of spin systems at equilibrium. We consider the Ising and the general O(N)symmetric universality class. For each of them, we review the estimates of the critical exponents, of the equation of state, of several amplitude ratios, and of the twopoint function of the order parameter. We report results in three and two dimensions. We discuss the crossover phenomena that are observed in this class of systems. In particular, we review the fieldtheoretical and numerical studies of systems with mediumrange interactions. Moreover, we consider several examples of magnetic and structural phase transitions, which are described by more complex LandauGinzburgWilson Hamiltonians, such as Ncomponent systems with cubic anisotropy, O(N)symmetric systems in the presence of quenched disorder, frustrated spin systems with noncollinear or canted order, and finally, a class of systems described by the tetragonal LandauGinzburgWilson Hamiltonian with three quartic couplings. The results for the tetragonal Hamiltonian are original, in particular we present the sixloop perturbative series for the βfunctions and the critical exponents.
Twocomponent spinor techniques and Feynman rules for quantum field theory and supersymmetry
, 2008
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HEISENBERG–EULER EFFECTIVE LAGRANGIANS: BASICS AND EXTENSIONS
, 2004
"... I present a pedagogical review of Heisenberg–Euler effective Lagrangians, beginning with the original work of Heisenberg and Euler, and Weisskopf, for the one loop effective action of quantum electrodynamics in a constant electromagnetic background field, and then summarizing some of the important a ..."
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Cited by 51 (2 self)
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I present a pedagogical review of Heisenberg–Euler effective Lagrangians, beginning with the original work of Heisenberg and Euler, and Weisskopf, for the one loop effective action of quantum electrodynamics in a constant electromagnetic background field, and then summarizing some of the important applications and generalizations to inhomogeneous background fields, nonabelian backgrounds, and higher loop effective Lagrangians.