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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.
On the ultraviolet problem for the 2D weakly interacting Fermi gas
, 2008
"... We prove that the effective potential of the twodimensional interacting continuous Fermi gas with infrared cutoff is an analytic function of the coupling strength near the origin. This is the starting point to study the infrared problem of the model without putting any ultraviolet cutoff, as usuall ..."
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Cited by 2 (0 self)
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We prove that the effective potential of the twodimensional interacting continuous Fermi gas with infrared cutoff is an analytic function of the coupling strength near the origin. This is the starting point to study the infrared problem of the model without putting any ultraviolet cutoff, as usually done in the literature. 1
Constructive Quantum Field Theory 1. Euclidean Quantum Fields
, 2005
"... The construction of a relativistic quantum field is still an open problem for fields in spacetime dimension d ≥ 4. The conceptual difficulty that sometimes led to fear an incompatibility between nontrivial quantum systems and special relativity has however been solved in the case of dimension d = 2, ..."
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The construction of a relativistic quantum field is still an open problem for fields in spacetime dimension d ≥ 4. The conceptual difficulty that sometimes led to fear an incompatibility between nontrivial quantum systems and special relativity has however been solved in the case of dimension d = 2, 3 although, so far, has not influenced the corresponding debate on the foundations of quantum mechanics, still much alive. It began in the early 1960’s with Wightman’s work on the axioms and the attempts at understanding the mathematical aspects of renormalization theory and with Hepps ’ renormalization theory for scalar fields. The breakthrough idea was, perhaps, Nelson’s realization that the problem could really be studied in Euclidean form. A solution in dimensions d = 2, 3 has been obtained in the 1960’s and 1970’s through a remarkable series of papers by Nelson, Glimm, Jaffe, Guerra. While the works of Nelson and Guerra relied on the “Euclidean approach ” (see below) and on d = 2 the early works of Glimm and Jaffe dealt with d = 3 making use of the “Minkowskian approach” (based on second quantization) but making already use of a multiscale analysis technique. The latter received great impulsion and systematization by the adoption of Wilson’s views and methods on renormalization: in Physics terminology renormalization group methods; a point of view taken
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