Using renormalization group methods, we study the Heisenberg-Ising XY Z chain in an external magnetic field directed as the z axis, in the case of small coupling J3 in the z direction. We study theâ€¦ (More)

Methods for the analysis of the Lindstedt series for KAM tori and renormalizability in classical mechanics A review with some applications Abstract: This paper consists in a unified exposition ofâ€¦ (More)

Systems of interacting non relativistic fermions in d = 1, as well as spin chains or interacting bidimensional Ising models, verify an hidden approximate Gauge invariance which can be used to deriveâ€¦ (More)

We construct a QFT for the Thirring model for any value of the mass in a functional integral approach, by proving that a set of Grassmann integrals converges, as the cutoffs are removed and for aâ€¦ (More)

It is widely believed that the critical properties of several planar lattice models, like the Eight Vertex or the Ashkin-Teller models, are well described by an effective Quantum Field Theoryâ€¦ (More)

The Ashkinâ€“Teller (AT) model is a generalization of Ising 2â€“d to a four states spin model; it can be written in the form of two Ising layers (in general with different couplings) interacting via aâ€¦ (More)

1.1 Anomalies in QFT. The chiral anomaly appears as a quantum correction to the conservation of the axial current for massless fermions. A crucial property is the anomaly nonrenormalization, whichâ€¦ (More)

We perform a rigorous computation of the specific heat of the Ashkin-Teller model in the case of small interaction and we explain how the universality-nonuniversality crossover is realized when theâ€¦ (More)

We investigate the properties of chiral anomalies in d = 2 in the framework of Constructive Quantum Field Theory. The condition that the gauge propagator is sufficiently soft in the ultraviolet isâ€¦ (More)

We give the first rigorous (non perturbative) proof of Luttinger liquid behavior in the one dimensional Hubbard model, for small repulsive interaction and values of the density different from halfâ€¦ (More)