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Constructive φ 4 field theory without tears
 Annales Henri Poincare
"... We propose to treat the φ 4 Euclidean theory constructively in a simpler way. Our method, based on a new kind of ”loop vertex expansion”, no longer requires the painful intermediate tool of cluster and Mayer expansions. 1 ..."
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Cited by 21 (5 self)
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We propose to treat the φ 4 Euclidean theory constructively in a simpler way. Our method, based on a new kind of ”loop vertex expansion”, no longer requires the painful intermediate tool of cluster and Mayer expansions. 1
Tree Quantum Field Theory
 Annales Henri Poincare 10 (2009) 867 [arXiv:0807.4122 [hepth
"... We propose a new formalism for quantum field theory (QFT) which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e. it computes correlation functions through convergent rather than divergent expansions. It applies both to Fermio ..."
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Cited by 10 (3 self)
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We propose a new formalism for quantum field theory (QFT) which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e. it computes correlation functions through convergent rather than divergent expansions. It applies both to Fermionic and Bosonic theories. It is compatible with the renormalization group, and it allows to define nonperturbatively differential renormalization group equations. It accommodates any general stable polynomial Lagrangian. It can equally well treat noncommutative models or matrix models such as the GrosseWulkenhaar model. Perhaps most importantly it removes the spacetime background from its central place in QFT, paving the way for a nonperturbative definition of field theory in noninteger dimension. I
I Renormalization of the 2point function of the Hubbard model at halffilling
, 2008
"... We prove that the Hubbard model at finite temperature T and halffilling is analytic in its coupling constant λ for λ  ≤ c/log T  2, where c is some numerical constant. We also bound the selfenergy and prove that the Hubbard model at halffilling is not a Fermi liquid (in the mathematically pr ..."
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Cited by 5 (3 self)
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We prove that the Hubbard model at finite temperature T and halffilling is analytic in its coupling constant λ for λ  ≤ c/log T  2, where c is some numerical constant. We also bound the selfenergy and prove that the Hubbard model at halffilling is not a Fermi liquid (in the mathematically precise sense of Salmhofer), modulo a simple lower bound on the first nontrivial selfenergy graph, which will be published in a companion paper.
I The Hubbard model at halffilling, part III: the lower
, 2008
"... We complete the proof that the twodimensional Hubbard model at halffilling is not a Fermi liquid in the mathematically precise sense of Salmhofer, by establishing a lower bound on a second derivative in momentum of the first nontrivial selfenergy graph. ..."
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We complete the proof that the twodimensional Hubbard model at halffilling is not a Fermi liquid in the mathematically precise sense of Salmhofer, by establishing a lower bound on a second derivative in momentum of the first nontrivial selfenergy graph.
Random matrices and the Anderson model
"... In recent years, constructive field techniques and the method of renormalization group around extended singularities have been applied to the weak coupling regime of the Anderson Model. It has allowed to clarify the relationship between this model and the theory of random matrices. We review this si ..."
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In recent years, constructive field techniques and the method of renormalization group around extended singularities have been applied to the weak coupling regime of the Anderson Model. It has allowed to clarify the relationship between this model and the theory of random matrices. We review this situation and the current program to analyze in detail the density of states and Green’s functions of this model using the supersymmetric formalism. 1
A RIGOROUS TREATMENT OF THE PERTURBATION THEORY FOR MANYELECTRON SYSTEMS
, 904
"... Four point correlation functions for many electrons at finite temperature in periodic lattice of dimension d ( ≥ 1) are analyzed by the perturbation theory with respect to the coupling constant. The correlation functions are characterized as a limit of finite dimensional Grassmann integrals. A lower ..."
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Four point correlation functions for many electrons at finite temperature in periodic lattice of dimension d ( ≥ 1) are analyzed by the perturbation theory with respect to the coupling constant. The correlation functions are characterized as a limit of finite dimensional Grassmann integrals. A lower bound on the radius of convergence and an upper bound on the perturbation series are obtained by evaluating the Taylor expansion of logarithm of the finite dimensional Grassmann Gaussian integrals. The perturbation series up to second order is numerically implemented along with the volumeindependent upper bounds on the sum of the higher order terms in 2 dimensional case.
unknown title
, 2012
"... Etude du modèle de Hubbard bidimensionnel à demiremplissage par des méthodes constructives ..."
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Etude du modèle de Hubbard bidimensionnel à demiremplissage par des méthodes constructives
Introduction to the Renormalization Group with Applications to NonRelativistic Quantum Electron Gases
, 2013
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