Critical properties of Φ1+14\Phi^4_{1+1}-theory in Light-Cone Quantization

The dynamics of the phase transition of the continuum $\Phi ^{4}_{1+1}$-theory in Light Cone Quantization is reexamined taking into account fluctuations of the order parameter $$ in the form of dynamical zero mode operators (DZMO) which appear in a natural way via the Haag expansion of the field $\Phi (x)$ of the interacting theory. The inclusion of the DZM-sector changes significantly the value of the critical coupling, bringing it in agreement within 2% with the most recent Monte-Carlo and high temperature/strong coupling estimates. The critical slowing down of the DZMO governs the low momentum behavior of the dispersion relation through invariance of this DZMO under conformal transformations preserving the local light cone structure. The critical exponent $\eta$ characterising the scaling behaviour at $k^2 \to 0$ comes out in agreement with the known value 0.25 of the Ising universality class. $\eta$ is made of two contributions: one, analytic $(75$) and another (25%) which can be evaluated only numerically with an estimated error of 3%. The $\beta$-function is then found from the non-perturbative expression of the physical mass. It is non-analytic in the coupling constant with a critical exponent $\omega=2$. However, at D=2, $\omega$ is not parametrisation independent with respect to the space of coupling constants due to this strong non-analytic behaviour.Comment: Latex, 22 pages, 8 Postscript figures,Appendi

Aspects de la quantification des théories de champs scalaires sur le cône de lumière

Light-cone quantization proceeds through Dirac's Front Form and needs a procedure for the handling of dynamical constranits. It is treated of The phi4 (1+1) theory is examined with the help of a continuum formulation of the fields and zero modes Haag expansion (CLCQ). This allowed an original solution of the equations of motion and the constraints, as well as a consistant infrared and ultraviolet divergences renormalization. Phase transition analysis shows second order non perturbative critical coupling constant similar to conventionnal methods fourth order results Comparative study of discrete and continuum Pauli-jordan commutator formulations demonstrates that violation of causality is nothing else a finite volume effect linked with zero modes substraction in discretes sums. The study of phi4 (3+1) O(N) theory is begun with order 3 fields and zero modes 1/sqrt(N) expansion which enables to get, up to the 1/N^3, the same conventionnal correlation functions obtained by path integration.La quantification sur le cône de lumière est une méthode de quantification opérant dans la Front Form de Dirac et nécessitant une procédure de traitement des contraintes dynamiques. Elle est abordée dans le cas de deux théories scalaires. La théorie phi4 (1+1) est examinée à l'aide d'une formulation continue du développement de Haag des champs et des modes zéros (CLCQ). Ceci permet une résolution originale des équations du mouvement et des contraintes ainsi qu'une renormalisation consistante des divergences infrarouges et ultraviolettes. L'analyse de la transition de phase fait apparaître au deuxième ordre un couplage critique non perturbatif de valeur analogue aux résultats du quatrième ordre des méthodes conventionnelles. L'étude comparée du commutateur de Pauli-Jordan dans les formulations discrètes et continues montre que la violation de causalité n'est qu'un pur effet de taille finie associé à la soustraction du mode zéro dans les sommes discrètes. L'étude de la théorie phi4 (3+1) O(N) est amorcée par le calcul des champs et des modes zéros à l'ordre 3 du développement en 1/sqrt(N) qui permet de retrouver jusqu'à l'ordre 1/N^3 les fonctions de corrélation conventionnelles obtenues par intégrales de chemin

Modelling and simulating new power grid control architectures

International audienceWith the growing number of distributed energy resources, electricity grids have a stronger need for resiliency that can be met by automation. Various architectures for such automated mechanisms are possible and they need to be systemat- ically evaluated. The NACRE platform, presented here, allows to model and simulate various control architectures and to evaluate their behaviors against different types of communication hazards. The first version of the platform is evaluated on a use case