Results 1  10
of
1,332
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 ..."
Abstract

Cited by 169 (28 self)
 Add to MetaCart
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 in Combinatorics, 2005, 173–226
"... ..."
(Show Context)
Local BRST cohomology in the antifield formalism. I. General theorems
 COMM. MATH. PHYS
, 1995
"... ..."
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 ..."
Abstract

Cited by 136 (17 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 63 (2 self)
 Add to MetaCart
(Show Context)
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.
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 ..."
Abstract

Cited by 61 (2 self)
 Add to MetaCart
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
Twocomponent spinor techniques and Feynman rules for quantum field theory and supersymmetry
, 2008
"... ..."
Nonperturbative renormalization flow in quantum field theory and statistical physics
, 2000
"... We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Nonperturbative solutions follow from approximations to the general form of the ..."
Abstract

Cited by 52 (0 self)
 Add to MetaCart
(Show Context)
We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Nonperturbative solutions follow from approximations to the general form of the coarsegrained free energy or effective average action. They interpolate between the microphysical laws and the complex macroscopic phenomena. Our approach yields a simple unified description for O(N)symmetric scalar models in two, three or four dimensions, covering in particular the critical phenomena for the secondorder phase transitions, including the KosterlitzThouless transition and the critical behavior of polymer chains. We compute the aspects of the critical equation of state which are universal for a large variety of physical systems and establish a direct connection between microphysical and critical quantities for a liquidgas transition. Universal features of firstorder phase transitions are studied in the context of scalar matrix models. We show that the quantitative treatment of coarse graining is essential for a detailed estimate of the nucleation rate. We discuss quantum statistics in thermal equilibrium or thermal quantum field theory with fermions and bosons and we describe the high temperature symmetry restoration in quantum field theories with spontaneous symmetry breaking. In particular we explore chiral symmetry breaking and the high temperature or high density chiral phase transition in quantum chromodynamics using models with effective fourfermion interactions.
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 ..."
Abstract

Cited by 52 (12 self)
 Add to MetaCart
(Show Context)
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.