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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
Estimates on Renormalization Group Transformations
 CAN. J. MATH
, 1996
"... We consider a specific realization of the renormalization group (RG) transformation acting on functional measures for scalar quantum fields which are expressible as a polymer expansion times an ultraviolet cutoff Gaussian measure. The new and improved definitions and estimates we present are suffi ..."
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Cited by 11 (3 self)
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We consider a specific realization of the renormalization group (RG) transformation acting on functional measures for scalar quantum fields which are expressible as a polymer expansion times an ultraviolet cutoff Gaussian measure. The new and improved definitions and estimates we present are sufficiently general and powerful to allow iteration of the transformation, hence the analysis of complete renormalization group flows, and hence the construction of a variety of scalar quantum field theories.
The Jacobian conjecture as a problem of perturbative quantum field theory, math.CO/0208173, preprint
, 2002
"... The Jacobian conjecture is an old unsolved problem in mathematics, which has been unsuccessfully attacked from many different angles. We add here another point of view pertaining to the so called formal inverse approach, that of perturbative quantum field theory. ..."
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Cited by 10 (3 self)
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The Jacobian conjecture is an old unsolved problem in mathematics, which has been unsuccessfully attacked from many different angles. We add here another point of view pertaining to the so called formal inverse approach, that of perturbative quantum field theory.
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
Mean Green's Function of the Anderson Model at Weak Disorder with an Infrared Cutoff
, 1999
"... In this paper we develop a polymer expansion with large/small field conditions for the mean resolvent of a weakly disordered system. Then we show that we can apply our result to a twodimensional model, for energies outside the unperturbed spectrum or in the free spectrum provided the potential has a ..."
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Cited by 10 (0 self)
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In this paper we develop a polymer expansion with large/small field conditions for the mean resolvent of a weakly disordered system. Then we show that we can apply our result to a twodimensional model, for energies outside the unperturbed spectrum or in the free spectrum provided the potential has an infrared cutoff. This leads to an asymptotic expansion for the density of states. We believe this is an important first step towards a rigorous analysis of the density of states in the free spectrum of a random Schrödinger operator at weak disorder. 1
Towards a complete renormalization group trajectory between two fixed points. In Oberwolfach report for the april 2006 meeting The Rigorous Renormalization Group
, 2006
"... Abstract. We give a rigorous nonperturbative construction of a massless discrete trajectory for Wilson’s exact renormalization group. The model is a three dimensional Euclidean field theory with a modified free propagator. The trajectory realizes the mean field to critical crossover from the ultravi ..."
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Cited by 9 (3 self)
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Abstract. We give a rigorous nonperturbative construction of a massless discrete trajectory for Wilson’s exact renormalization group. The model is a three dimensional Euclidean field theory with a modified free propagator. The trajectory realizes the mean field to critical crossover from the ultraviolet Gaussian fixed point to an analog recently constructed by Brydges, Mitter and Scoppola of the WilsonFisher nontrivial fixed point.
Constructive field theory in zero dimension
, 2009
"... Constructive field theory can be considered as a reorganization of perturbation theory in a convergent way. In this pedagogical note we propose to wander through five different methods to compute the number of connected graphs of the zerodimensional φ 4 field theory, in increasing order of sophisti ..."
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Cited by 6 (3 self)
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Constructive field theory can be considered as a reorganization of perturbation theory in a convergent way. In this pedagogical note we propose to wander through five different methods to compute the number of connected graphs of the zerodimensional φ 4 field theory, in increasing order of sophistication and power.
A single slice 2d Anderson model at weak disorder, Ecole Polytechnique preprint
"... We introduce a matrixoperator formulation of the Anderson model in d = 2. In a single slice, we can then derive an analogy between our model and a standard random matrices problem. This enable us to construct and control the Green function in one slice which is an important prerequisite to a full m ..."
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Cited by 2 (1 self)
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We introduce a matrixoperator formulation of the Anderson model in d = 2. In a single slice, we can then derive an analogy between our model and a standard random matrices problem. This enable us to construct and control the Green function in one slice which is an important prerequisite to a full multiscale study of the problem using the Renormalization Group approach. 1