Renormalization Group Improved Optimized Perturbation Theory: Revisiting the Mass Gap of the O(2N) Gross-Neveu Model

We introduce an extension of a variationally optimized perturbation method, by combining it with renormalization group properties in a straightforward (perturbative) form. This leads to a very transparent and efficient procedure, with a clear improvement of the non-perturbative results with respect to previous similar variational approaches. This is illustrated here by deriving optimized results for the mass gap of the O(2N) Gross-Neveu model, compared with the exactly know results for arbitrary N. At large N, the exact result is reproduced already at the very first order of the modified perturbation using this procedure. For arbitrary values of N, using the original perturbative information only known at two-loop order, we obtain a controllable percent accuracy or less, for any N value, as compared with the exactly known result for the mass gap from the thermodynamical Bethe Ansatz. The procedure is very general and can be extended straightforwardly to any renormalizable Lagrangian model, being systematically improvable provided that a knowledge of enough perturbative orders of the relevant quantities is available.Comment: 18 pages, 1 figure, v2: Eq. (4.5) corrected, comments adde

Trente années au service du financement de l’agriculture

Banquier historique de l’agriculture, le Crédit agricole a progressivement modifié ses méthodes de financement. Il a pu ainsi mieux répondre aux nouveaux besoins des exploitants agricoles et aux évolutions rapides de ce secteur. Après la banalisation des prêts bonifiés par l’Etat en 1989, le Crédit agricole a aussi adopté une politique commerciale plus efficace. André Neveu, ancien responsable du marché des agriculteurs à la CNCA, nous retrace les grandes lignes de cette évolutionThe Credit Agricole, as a historical banker of agriculture, has gradually modified its financing methods. Thus it has been able to meet the new needs of the farmers and of this quick changing activity. After the government allowed other banks to grant subsidized loans in 1989, the Credit Agricole took up a more efficient commercial policy. André Neveu, a former chief executive in charge of the agricultural market at the Credit Agricole relates the major steps of this evolution

Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks

Liouville field theory on a sphere is considered. We explicitly derive a differential equation for four-point correlation functions with one degenerate field $V_{-\frac{mb}{2}}$. We introduce and study also a class of four-point conformal blocks which can be calculated exactly and represented by finite dimensional integrals of elliptic theta-functions for arbitrary intermediate dimension. We study also the bootstrap equations for these conformal blocks and derive integral representations for corresponding four-point correlation functions. A relation between the one-point correlation function of a primary field on a torus and a special four-point correlation function on a sphere is proposed

A new improved optimization of perturbation theory: applications to the oscillator energy levels and Bose-Einstein critical temperature

Improving perturbation theory via a variational optimization has generally produced in higher orders an embarrassingly large set of solutions, most of them unphysical (complex). We introduce an extension of the optimized perturbation method which leads to a drastic reduction of the number of acceptable solutions. The properties of this new method are studied and it is then applied to the calculation of relevant quantities in different $\phi^4$ models, such as the anharmonic oscillator energy levels and the critical Bose-Einstein Condensation temperature shift $\Delta T_c$ recently investigated by various authors. Our present estimates of $\Delta T_c$, incorporating the most recently available six and seven loop perturbative information, are in excellent agreement with all the available lattice numerical simulations. This represents a very substantial improvement over previous treatments.Comment: 9 pages, no figures. v2: minor wording changes in title/abstract, to appear in Phys.Rev.

Dix ans d'histoire culturelle

L'association pour le développement de l'histoire culturelle (ADHC) est née, en 1999, du constat de la place croissante, en même temps que problématique, de l'histoire culturelle dans l'historiographie contemporaine. Revendiquée par les uns, dénoncée par les autres, cette place méritait l'institution d'un lieu de rencontres où tous ceux qui se reconnaissent dans cette qualification pourraient échanger sur le fond et sur la forme de leur travail. L'association a tenu son premier congrès en 2000. Au terme d'une décennie et plus d'activité, il était temps de tirer le bilan et, comme il se doit, de tracer de nouvelles perspectives. Cette anthologie des conférences et tables rondes organisées dans le cadre du congrès annuel de l'association propose un panorama unique en son genre des propositions avancées par l'histoire culturelle en France et, dans une moindre mesure, à l'étranger depuis dix ans. Regroupés en sections thématiques (définitions et frontières, objets, regards et transferts, débats), ces textes rédigés par d'éminents spécialistes venus de divers horizons (historiens, sociologues, philosophes, historiens de l'art ou de la littérature) donnent à voir à la fois la permanence de certains questionnements et leur renouvellement

Réforme de la Politique Agricole Commune : impact sur les modalités de financement de l'agriculture

[eng] Reform of the common agricultural policy : consequences on the ways of financing agriculture . The Reform of the Common Agricultural Policy will urge farm banks to adapt their intervention means. Thus they will take into account the new market environment and the numerous situations : serious structural problems or minor conjonctural adjustments. Later on, the new projects will have to be scanned with the greatest care because their profitability might slump. [fre] La réforme de la Politique Agricole Commune va conduire les banquiers de l'agriculture à adapter leur modalité d'intervention pour tenir compte du nouveau contexte de marché et de la diversité des situations : difficultés structurelles graves ou simples ajustements conjoncturels. Ultérieurement, les projets nouveaux devront être examinés avec la plus grande attention car leur rentabilité risque de se réduire dangereusement.