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Thesis (Ph. D.)--California Institute of Technology, 1998. UM #9912868. / Advisor names found in the Acknowledgments pages of the thesis. Title from home page. Viewed 01/20/2010. Includes bibliographical references.

published_or_final_version / Physics / Doctoral / Doctor of Philosophy

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Orientador: José Francisco Gomes / Banca: Luiz Agostinho Ferreira / Banca: Francesco Toppan / Banca: Marco Aurélio Cattacin Kneipp / Banca: Clisthenis Ponce Constantinidis / Resumo: Nessa tese se constrói o funcional de ação dos modelos de Toda supersimétricos afins e se deduzem as transformações de supersimétria dos modelos desde o ponto de vista de fluxos de simetria Fermionicos. A integrabilidade é definida em termos de um problema de fatorização de Riemann-Hilbert estendido que unifica parâmetros de evolução Abelianos e não Abelianos. Se introduzem modelos integráveis puramente Fermionicos definidos em supercosets onde toda a parte Bosonica é completamente eliminada. Vários exemplos são considerados / Abstract: In this thesis we construct the action functional for the supersymmetric affine Toda models and deduce the supersymmetry transformations of the models from the point of view of Fermionic symmetry flows. The underlying Integrability is defined in terms of an extended Riemann-Hilbert factorization problem which unifies Abelian and non-Abelian evolution parameters. We also introduce purely Fermionic Integrable models defined on supercosets where the Bosonic part is completely eliminated. Several examples are consider / Doutor

O movimento de três partículas idênticas e sem spin em uma dimensão é o objeto de estudo neste trabalho. As equações de Faddeev que descrevem o espalhamento de uma partícula por um estado ligado de duas partículas é estudado extendendo-se analiticamente um dos momentos para todo o plano complexo (chamado de método de Brayshaw). Encontramos que quando um subsistema de duas partículas apresenta um estado ligado com energia V0, o sistema de três partículas correspondente apresentará um estado ligado com energia 4 V0. Também concluímos que se um subsistema de duas partículas apresenta uma ressonância para uma energia V0, o mesmo não ocorre no sistema de três partículas. Estes resultados resolvem uma longa controvérsia na literatura. / The one dimension motion of three identical spinless particles is studied here. The Faddeev equations describing the scattering of one particle by a two particle bound-state is studied by extending analytically one of the momenta to the whole complex plane (Brayshaw\'s method). It is found that to a bound-state of energy V0 in the two particle subsystem corresponds a bound-state of energy 4V0 in the three particle system. It is also found that if the two particle subsystem has a resonance pole at V0 it does not follows that there is .a resonance in the three particle system. These results solve a long standing controversy in the literature.

Generalized geometry is a recently discovered branch of differential geometry that has received a reasonable amount of interest due to the emergence of several connections with areas of Mathematical Physics. The theory is also of interest because the different geometrical structures are often generalizations of more familiar geometries. We provide an introduction to the theory which explores a number of these generalized geometries. After introducing the basic underlying structures of generalized geometry we look at integrability which offers some geometrical insight into the theory and this leads to Dirac structures. Following this we look at generalized metrics which provide a generalization of Riemannian metrics. We then look at generalized complex geometry which is a generalization of both complex and symplectic geometry and is able to unify a number of features of these two structures. Beyond generalized complex geometry we also look at generalized Calabi-Yau and generalized Kähler structures which are also generalizations of the more familiar structures. / Thesis (M.Sc.(M&CS))--University of Adelaide, School of Mathematical Sciences, Discipline of Pure Mathematics, 2007.

La production de dileptons en collisions d'ions lourds relativistes (CERN/SPS, SIS/ HADES, RHIC) et le comportement des mésons vecteurs (en particulier le méson $\rho$) consti­tuent un des sujets centraux de la chromodynamique quantique (QCD) dans la matière <br />hadronique dense et chaude. Un enjeu crucial est en effet l'étude de la restauration partielle ou totale de la symétrie chirale SU(2) x SU(2), ce qui nécessite en pratique l'utilisation de théories effectives. Une des difficultés majeures est de construire une telle théorie qui, s'appuyant sur des contraintes phénoménologiques bien établies à basse température et/ou densité, permette d'obtenir des prédictions lorsque l'on se rapproche de la transition de phase.<br />Le modèle qui a été utilisé (développé par M. Urban) est basé sur l'idée du modèle sigma linéaire jaugé (mésons $\rho et $\alpha$1 ) mais adapté de façon très détaillée à la phénoménologie en ne gardant que de façon approximative la symétrie locale. Une partie importante de ce travail a consisté à régulariser la théorie, c'est ­à­dire à s'affranchir des divergences qui apparaissent dans les calculs à une boucle. Nous avons donc été amenés à introduire une <br />nouvelle prescription de coupure des intégrales qui fasse apparaître explicitement un cut­ off tout en respectant les symétries des modèles étudiés. Afin de tester la validité de cette méthode, nous l'avons appliquée à QED en 4 et 5 dimensions. Pour finir, nous avons établi les équations du groupe de renormalisation dans notre modèle chiral particulier et avons montré que même si la manifestation vectorielle introduite récemment dans la littérature <br />était compatile avec nos équations, la restauration "traditionnelle'' à la Ginzburg-­Landau était plus probable.

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