Constructive Field Theory in Zero Dimension (2009)
In this pedagogical note we propose to wander through five different methods to compute the number of connected graphs of the zero-dimensional $\phi^4$ field theory,in increasing order of...
Topological Graph Polynomials and Quantum Field Theory, Part I: Heat Kernel Theories (2008)
Krajewski, T., Rivasseau, V., Tanasa, A., Wang, Zhituo
We investigate the relationship between the universal topological polynomials for graphs in mathematics and the parametric representation of Feynman amplitudes in quantum field theory. In this first...
Tree Quantum Field Theory (2008)
Gurau, R., Magnen, J., Rivasseau, V.
We propose a new formalism for quantum field theory which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e. it computes...
Non Commutative Field Theory on Rank One Symmetric Spaces (2008)
Bieliavsky, P., Gurau, R., Rivasseau, V.
Quantum field theory has been shown recently renormalizable on flat Moyal space and better behaved than on ordinary space-time. Some models at least should be completely finite, even beyond...
A translation-invariant renormalizable non-commutative scalar model (2008)
Gurau, R., Magnen, J., Rivasseau, V., Tanasa, A.
In this paper we propose a translation-invariant scalar model on the Moyal space. We prove that this model does not suffer from the UV/IR mixing and we establish its renormalizability to all orders...
Bosonic Monocluster Expansion (2007)
A. Abdesselam, J. Magnen, V. Rivasseau
We compute connected Green's functions of a Bosonic field theory with cutoffs by means of a "minimal " expansion which in a single move, interpolating a generalized propagator,...
Vanishing of Beta Function of Non Commutative $\Phi^4_4$ Theory to all orders (2007)
Disertori, M., Gurau, R., Magnen, J., Rivasseau, V.
The simplest non commutative renormalizable field theory, the $\phi_4$ model on four dimensional Moyal space with harmonic potential is asymptotically safe up to three loops, as shown by H. Grosse...
Constructive $\phi^4$ field theory without tears (2007)
We propose to treat the $\phi^4$ 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...
Constructive Matrix Theory (2007)
We extend the technique of constructive expansions to compute the connected functions of matrix models in a uniform way as the size of the matrix increases. This provides the main missing ingredient...
Non-Commutative Complete Mellin Representation for Feynman Amplitudes (2007)
Gurau, R., Malbouisson, A. P. C., Rivasseau, V., Tanasa, A.
We extend the complete Mellin (CM) representation of Feynman amplitudes to the non-commutative quantum field theories. This representation is a versatile tool. It provides a quick proof of meromorphy...
Non-Commutative Complete Mellin Representation for Feynman Amplitudes (2007)
Gurau, R., Malbouisson, A. P. C., Rivasseau, V., Tanasa, A.
We extend the complete Mellin (CM) representation of Feynman amplitudes to the non-commutative quantum field theories. This representation is a versatile tool. It provides a quick proof of meromorphy...
Non-Commutative Renormalization (2007)
Rivasseau, V., Vignes-Tourneret, F.
We review the recent approach of Grosse and Wulkenhaar to the perturbative renormalization of non commutative field theory and suggest a related constructive program. This paper is dedicated to J....
Constructive Field Theory and Applications: Perspectives and Open Problems (2007)
In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future...
Vanishing of Beta Function of Non Commutative $\Phi^4_4$ Theory to all orders (2006)
Disertori, M., Gurau, R., Magnen, J., Rivasseau, V.
The simplest non commutative renormalizable field theory, the $\phi_4$ model on four dimensional Moyal space with harmonic potential is asymptotically safe up to three loops, as shown by H. Grosse...
Explicit Fermionic Tree Expansions (2006)
We express connected Fermionic Green's functions in terms of completely explicit tree formulas. In contrast with the ordinary formulation in terms of Feynman graphs these formulas allow a completely...
An Explicit Large Versus Small Field Multiscale Cluster Expansion (2006)
We introduce a new type of cluster expansion which generalizes a previous formula of Brydges and Kennedy. The method is especially suited for performing a phase-space multiscale expansion in a just...
Trees, forests and jungles: a botanical garden for cluster expansions (2006)
Combinatoric formulas for cluster expansions have been improved many times over the years. Here we develop some new combinatoric proofs and extensions of the tree formulas of Brydges and Kennedy, and...
Bosonic Monocluster Expansion (2006)
Abdesselam, A., Magnen, J., Rivasseau, V.
We compute connected Green\'s functions of a Bosonic field theory with cutoffs by means of a ``minimal\'\' expansion which in a single move, interpolating a generalized propagator, performs the usual...
Renormalization of noncommutative phi 4-theory by multi-scale analysis (2006)
Rivasseau, V., Vignes-Tourneret, F., Wulkenhaar, R.
In this paper we give a much more efficient proof that the real Euclidean phi 4-model on the four-dimensional Moyal plane is renormalizable to all orders. We prove rigorous bounds on the propagator...
Propagators for Noncommutative Field Theories (2005)
Gurau, R., Rivasseau, V., Vignes-Tourneret, F.
In this paper we provide exact expressions for propagators of noncommutative Bosonic or Fermionic field theories after adding terms of the Grosse-Wulkenhaar type in order to ensure Langmann-Szabo...
Renormalization of noncommutative phi 4-theory by multi-scale analysis (2005)
Rivasseau, V., Vignes-Tourneret, F., Wulkenhaar, R.
In this paper we give a much more efficient proof that the real Euclidean phi 4-model on the four-dimensional Moyal plane is renormalizable to all orders. We prove rigorous bounds on the propagator...
Renormalization of noncommutative phi 4-theory by multi-scale analysis (2005)
Rivasseau, V., Vignes-Tourneret, F., Wulkenhaar, R.
In this paper we give a much more efficient proof that the real Euclidean phi 4-model on the four-dimensional Moyal plane is renormalizable to all orders. We prove rigorous bounds on the propagator...
Renormalization of noncommutative phi 4-theory by multi-scale analysis (2005)
Rivasseau, V., Vignes-Tourneret, F., Wulkenhaar, R.
In this paper we give a much more efficient proof that the real Euclidean phi 4-model on the four-dimensional Moyal plane is renormalizable to all orders. We prove rigorous bounds on the propagator...
Non-Commutative Renormalization (2004)
Rivasseau, V., Vignes-Tourneret, F.
We review the recent approach of Grosse and Wulkenhaar to the perturbative renormalization of non commutative field theory and suggest a related constructive program. This paper is dedicated to J....
Random Matrices and the Anderson Model (2003)
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...
Supersymmetric Analysis of a Simplified Two Dimensional Anderson Model at Small Disorder (2002)
Bellissard, J., Magnen, J., Rivasseau, V.
This work proposes a very simple random matrix model, the Flip Matrix Model, liable to approximate the behavior of a two dimensional electron in a weak random potential. Its construction is based on...
Bosonic Monocluster Expansion (2002)
Abdesselam, A., Magnen, J., Rivasseau, V.
We compute connected Green\'s functions of a Bosonic field theory with cutoffs by means of a ``minimal\'\' expansion which in a single move, interpolating a generalized propagator, performs the usual...
Disertori, M., Magnen, J., Rivasseau, V.
In this paper we complete the first step, namely the uniform bound on completely convergent contributions, towards proving that a three dimensional interacting system of Fermions is a Fermi liquid in...
Constructive Field Theory and Applications: Perspectives and Open Problems (2000)
In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future...
Bosonic Monocluster Expansion (2000)
Abdesselam, A., Magnen, J., Rivasseau, V.
We compute connected Green's functions of a Bosonic field theory with cutoffs by means of a ``minimal'' expansion which in a single move, interpolating a generalized propagator, performs the usual...
Bosonic Monocluster Expansion (2000)
Abdesselam, A., Magnen, J., Rivasseau, V.
We compute connected Green\'s functions of a Bosonic field theory with cutoffs by means of a ``minimal\'\' expansion which in a single move, interpolating a generalized propagator, performs the usual...
A Rigorous Proof of Fermi Liquid Behavior for Jellium Two-Dimensional Interacting Fermions (1999)
Using the method of continuous constructive renormalization group around the Fermi surface, it is proved that a jellium two-dimensional interacting system of Fermions at low temperature $T$ remains...
Interacting Fermi liquid at finite temperature: Part I: Convergent Attributions (1999)
Using the method of continuous renormalization group around the Fermi surface, we prove that a two-dimensional jellium interacting system of Fermions at low temperature T is a Fermi liquid (analytic...
Interacting Fermi liquid in two dimensions at finite temperature: Part II: Renormalization (1999)
This is a companion paper to cond-mat/9907130. Using the method of continuous renormalization group around the Fermi surface and the results of cond-mat/9907130, we achieve the proof that a...
Constructive Renormalization Theory (1999)
These notes are the second part of a common course on Renormalization Theory given with Professor P. da Veiga at X Jorge Andre Swieca Summer School, Aguas de Lindoia, Brazil, February 7-12, 1999. I...
Continuous Constructive Fermionic Renormalization (1998)
We build the two dimensional Gross-Neveu model by a new method which requires neither cluster expansion nor discretization of phase-space. It simply reorganizes the perturbative series in terms of...
Explicit Fermionic Tree Expansions (1997)
We express connected Fermionic Green's functions in terms of completely explicit tree formulas. In contrast with the ordinary formulation in terms of Feynman graphs these formulas allow a completely...
Explicit Fermionic Tree Expansions (1997)
We express connected Fermionic Green's functions in terms of completely explicit tree formulas. In contrast with the ordinary formulation in terms of Feynman graphs these formulas allow a completely...
Explicit Fermionic Tree Expansions (1997)
We express connected Fermionic Green's functions in terms of completely explicit tree formulas. In contrast with the ordinary formulation in terms of Feynman graphs these formulas allow a completely...
The Anderson Model as a Matrix Model (1996)
Magnen, J., Poirot, G., Rivasseau, V.
In this paper we describe a strategy to study the Anderson model of an electron in a random potential at weak coupling by a renormalization group analysis. There is an interesting technical analogy...
An Explicit Large Versus Small Field Multiscale Cluster Expansion (1996)
We introduce a new type of cluster expansion which generalizes a previous formula of Brydges and Kennedy. The method is especially suited for performing a phase-space multiscale expansion in a just...
An Explicit Large Versus Small Field Multiscale Cluster Expansion (1996)
We introduce a new type of cluster expansion which generalizes a previous formula of Brydges and Kennedy. The method is especially suited for performing a phase-space multiscale expansion in a just...
An Explicit Large Versus Small Field Multiscale Cluster Expansion (1996)
We introduce a new type of cluster expansion which generalizes a previous formula of Brydges and Kennedy. The method is especially suited for performing a phase-space multiscale expansion in a just...
Trees, forests and jungles: a botanical garden for cluster expansions (1994)
Combinatoric formulas for cluster expansions have been improved many times over the years. Here we develop some new combinatoric proofs and extensions of the tree formulas of Brydges and Kennedy, and...
Trees, forests and jungles: a botanical garden for cluster expansions (1994)
Combinatoric formulas for cluster expansions have been improved many times over the years. Here we develop some new combinatoric proofs and extensions of the tree formulas of Brydges and Kennedy, and...
Trees, forests and jungles: a botanical garden for cluster expansions (1994)
Combinatoric formulas for cluster expansions have been improved many times over the years. Here we develop some new combinatoric proofs and extensions of the tree formulas of Brydges and Kennedy, and...
Trees, Forests and Jungles: A Botanical Garden for Cluster Expansions (1994)
Combinatoric formulas for cluster expansions have been improved many times over the years. Here we develop some new combinatoric proofs and extensions of the tree formulas of Brydges and Kennedy, and...