J. Magnen
Starting from H. Fr\"ohlich's second-quantized Hamiltonian for a $d$-dimensional electron gas in interaction with lattice phonons describing the quantum vibrations of a metal, we present a rigorous mathematical derivation of the…
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 the sense of Salmhofer. The analysis…
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 correlation functions through convergent rather…
Let $B=(B_1(t),\ldots,B_d(t))$ be a $d$-dimensional fractional Brownian motion with Hurst index $\alpha<1/4$. Defining properly iterated integrals of $B$ is a difficult task because of the low H\"older regularity index of its paths. Yet…
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 tasks of the cluster and Mayer expansion.…
Recently Neumayr and Metzner have shown that the connected N-point density- correlation functions of the two-dimensional and the one-dimensional Fermi gas at one-loop order generically vanish/are regular in the small momentum/small…
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 between this problem and the theory of…
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 cluster and Mayer expansions.
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 in perturbation theory.
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 and R. Wulkenhaar, M. Disertori and 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 a phase space analysis, a suitable…