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Les facteurs de forme et les fonctions de corrélation déterminent les quantités dynamiques mesurables associées aux modèles de théorie des champs et de mécanique statistique. Dans le cas de modèles intégrables en dimension 2, au-delà des propriétés du spectre ou de la fonction de partition, un des grands défis actuels concerne le calcul exact des facteurs de forme et des fonctions de corrélation.Le but de cette thèse est de développer une approche permettant de résoudre ce problème dans le cadre de la méthode de séparation des variables quantique de Skyanin. Cette méthode généralise au cas quantique et pour des systèmes avec un grand nombre de degrés de liberté la méthode de Hamilton-Jacobi en mécanique analytique. Le Hamiltonien est exprimé avec des opérateurs séparés, son spectre et ses états propres caractérisés par un système d'équations de Baxter résultant des structures algébriques de Yang-Baxter, caractéristiques de l'intégrabilité de ces modèles.Cette thèse a permis, pour les modèles de sine-Gordon (théorie des champs quantique) et de Potts chiral (modèle de physique statistique), le calcul des produits scalaires entre états propres du Hamiltonien, la résolution du problème inverse, i. e. l'expression des opérateurs du modèle en termes des variables séparées, ainsi que le calcul en termes de déterminants des facteurs de forme, i. e. des éléments de matrice des opérateurs locaux du modèle dans la base propre du Hamiltonien, ce qui constitue un pas important vers le calcul des fonctions de corrélation de ces modèles. / Form factors and correlation functions determine the measurable dynamic quantities that are associated with field theories and statistical physics models. In the case of 2-dimensional integrable models, one of the main challenges beyond spectrum properties and partition function is the exact computation of form factors and correlation functions.The aim of this thesis is to develop an approach in the framework of Sklyanin's separation of variables to address this problem. This framework generalizes to the quantum case and for systems with many degrees of freedom the Hamilton-Jacobi method from analytical mechanics. The Hamiltonian is expressed in terms of separated operators, its spectrum and eigenvectors are characterized by a system of Baxter equations. These Baxter equations are a consequence of Yang-Baxter relations that are characteristic of these models being integrable.The result of this thesis is, in the case of the sine-Gordon model (quantum field theory) and of the chiral Potts model (statistical physics model), the computation of scalar products of Hamiltonian eigenstates, the resolution of the inverse problem (expressing the model operators in terms of separated variables) and the computation in terms of determinant of form factors (the matrix elements of the model local operators in the Hamiltonian eigenbasis), which is an important step towards the computation of the correlation functions of these models.

On étudie les théories de Yang-Mills. Pour ce faire, nous appliquons une nouvelle procédure de fixation de jauge qui vise à prendre en compte la présence des copies de Gribov. Ces copies correspondent à des solutions supplémentaires de la condition de jauge et ne sont pas prises en compte dans la procédure standard de Faddeev-Popov. Cette nouvelle procédure de fixation de jauge a d'abord été implémenté dans la jauge de Landau, où le régime de basse énergie a pu être étudié simplement par la théorie de perturbation et les propagateurs des gluons et des ghosts ont été trouvé en bon accord avec les résultats du réseau. Dans une première partie, nous appliquons cette procédure à une classe de jauges covariantes et non-linéaires (les jauges de Curci-Ferrari-Delbourgo-Jarvis). Nous montrons que ces jauges sont renormalisables en dimension quatre et donnons explicitement les expressions des constantes de renormalisation à une boucle. Nous calculons en théorie de perturbation les propagateurs de la théorie à l'ordre d'une boucle et implémentons le groupe de renormalisation. La seconde partie concerne l'étude du cas à température finie et de la transition de phase confinement-déconfinement. Nous travaillons dans une extention massive de la jauge de Landau-DeWitt. Nous calculons les propagateurs à une boucle et montrons qu'ils présentent de clairs signaux de la transition de phase à la différence de la jauge de Landau. / We investigate Yang-Mills theories. In particular, we follow a recently proposed new gauge-fixing procedure that aims at dealing with the presence of the so-called Gribov copies. These copies correspond to additional solutions to the gauge equation that are disregarded in the standard Faddeev-Popov procedure. This novel gauge-fixing approach was first implemented in the Landau gauge, where the low momentum regime was investigable by means of simple perturbation theory and the one-loop gluon and ghost propagators were found in good agreement with lattice results. In a first part, we extend this proposal to a class of nonlinear covariant (the Curci-Ferrari-Delbourgo-Jarvis) gauges . We prove that these gauges are renormalizable in four dimensions. We provide explicit expression of the renormalization constants at one-loop order. Then we compute the various propagators of the theory at one-loop order with and without renormalization group improvement. The second part of the thesis concerns the finite temperature case and in particular the study of the confinement-deconfinement phase transition. We work in the Landau-DeWitt gauge (a background extention of the Landau gauge) which allows for an explicit presence of an order parameter of the phase transition. This gauge is implemented following the previous gauge-fixing procedure. In particular it has been shown that the phase transition can be studied in perturbation theory. Here, we compute at one-loop order the gluon and ghost propagators (for SU(2) gauge group) and show that they display strong signals of the phase transition. This is to be put in regards with the results obtained for the Landau gauge propagators.

La correspondance AdS/CFT est la première réalisation précise de la dualité jauge/gravité. Jusqu’à maintenant la correspondance AdS/CFT reste une conjecture. La dualité de N = 4 SYM et la théorie des cordes est un exemple le plus notable de correspondance AdS/CFT. Un des obstacles principaux à l’explorer est le fait que le régime de couplage faible pour la théorie de jauge est le régime de couplage fort pour la théorie des cordes et vice versa. Par conséquent, aussi longtemps que les méthodes perturbatives sont appliquées, on ne peut pas comparer les observables de deux cotés de la correspondance directement en dehors de quelques cas particuliers. A ce stade, l’énorme symétrie de N = 4 SYM joue un rôle important en permettant le calcul exact des observables de la théorie au moins dans la limite planaire. Cette thèse est consacrée au calcul des fonctions à trois, l’un des principaux observables de N = 4 SYM, et est composée de deux parties. Dans la première partie nous considérons l’approche générale pour le calcul des fonctions à trois points sur la base de soi-disant vertex de spin, qui est inspiré de la théorie de champs des cordes. Dans la deuxième partie, nous considérons un type spécifique de fonctions à trois points appelés lourd-lourd-léger, qui sont caractérisés par la propriété que la longueur de l’un des opérateurs est beaucoup plus petite des longueurs de deux autres. Il s’avère que ces fonctions de corrélations peuvent être identifiées à des facteurs de forme diagonaux et ainsi on peut appliquer les résultats concernant les facteurs de forme. / N=4 SYM theory has been drawing the attention of a lot of physicists during two last decades mainly due to the two aspects: AdS/CFT correspondence and integrability. AdS/CFT correspondence is the first precise realization of the gauge/string duality whose history starts in the 60's, when a string theory was considered as a candidate for describing the strong interactions. In 1997 Maldacena made a proposal about the duality between certain conformal field theories (CFT) and string theories defined on the product of AdS space and some compact manifold, which implies a one to one map between the observables of the gauge and string counterparts. Up to now AdS/CFT correspondence still remains a conjecture. The duality of N=4 SYM and the appropriate string counterpart is the most notable example of the AdS/CFT correspondence. One of the main obstructions to exploring it is the fact that weak coupling regime for the gauge theory is the strong coupling regime for the string theory and vice versa. Therefore as long as perturbative methods are applied, one can not compare the observables of dual counterparts directly apart from some specific cases. At this point the huge symmetry of N=4 SYM plays an important role allowing exact computation of the theory observables at least in the planar limit. This property of the theory is called integrability. The observables of the N=4 SYM are Wilson loops and correlation functions built out of gauge invariant operators. The space-time dependence of the two- and three-point correlators is fixed by the conformal symmetry up to some parameters: dimensions of the operators in the case of two-point functions and dimensions of the operators and structure constants in the case of three-point functions. It's commonly accepted to refer to the problem of finding the dimensions of the operators as the spectral problem. On the classical level the operator dimension is equal to the sum of the dimensions of the fundamental fields out of which the operator is composed. When the interaction is turned on, the conformal dimension gets quantum correction. In order to compute three-point functions, apart from the conformal dimensions of corresponding operators one needs to compute the structure constants. In CFT computation of the higher-point correlators eventually can be reduced to computation of two- and three-point functions by means of the operator product expansion. Therefore two- and three-point functions appear to be building blocks of any correlator of the theory. This thesis is devoted to computation of three-point functions and consists of two parts. In the first part we consider the general approach for computing three-point functions based on the so-called spin vertex, which is inspired from the string field theory. In the second part we consider a specific kind of three-point functions called heavy-heavy-light, which are characterized by the property that the length of one of the operators is much smaller the lengthes of other two. It happens that this kind of correlators can be considered as diagonal form factors which supposes that in this case one can apply the results obtained in the form factor theory.

<p>We have studied fundamental aspects of time-resolved two-photon excited fluorescence depolarisation. The thesis presents experimental as well as theoretical progress. We show that a multi-photon induced instrumental response function obtained from a suspension of gold nanoparticles is appropriate for the analysis of two-photon excited fluorescence decays obtained using time-correlated single photon counting detection. Theoretical expressions have been derived for the fluorescence anisotropy decay obtained upon two-photon excitation of various molecular systems in liquid solutions: a) an anisotropic rigid rotor that undergoes rotational diffusion in the presence of ultrafast unresolved restricted reorientations, e.g. librations. b) a molecular group covalently attached to a stationary macromolecule, and undergoing local reorientation in a uniaxial ordering potential. A new approach to the analysis of two-photon excited fluorescence depolarisation experiments was developed, which combines data obtained by using linearly and circularly polarised excitation light, in a global manner. In the analysis, knowledge about unresolved reorientations was obtained from one-photon excitation studies of the corresponding systems. By means of this procedure it has been possible to obtain quantitative information about the molecular two-photon absorption tensor for perylene and two of its derivatives. Thereby the symmetry of the final excited and intermediate vibronic states could be assigned. The analysis reveals that the two-photon transition studied with the 800 nm laser exhibits mixed character. An important finding from the experiments was that the two-photon absorption tensor appears to be solvent dependent. Furthermore, the thesis presents the first theoretical treatment of two-photon excited donor-donor energy migration in the presence of molecular reorientation and which applies the extended Förster theory. Explicit expressions for molecules that belong to the point groups D_2h, D₂ and C_2v are given. Preliminary experiments are finally also reported on a two-photon excited donor-donor energy migration system consisting of a bisanthryl-bisteroid. </p>

Em uma detalhada revisão nós obtemos a lei do semi-círculo para a densidade de estados no ensemble gaussiano de Wigner. Também falamos sobre a analogia eletrostática de Dyson, enxergando os autovalores como cargas que se repelem no círculo unitário, mostrando que nesse caso a densidade de estados é uniforme. Em um contexto mais geral nós obtemos a lei do semicírculo, provando o teorema de Glivenko-Cantelli para variáveis fortemente correlacionadas usando um método combinatorial de contagem de trajetos, o que nos dá subsídios para falar em estabilidade da lei do semi-círculo. Também, nesta dissertação nós estudamos as funções de correlação nos ensembles gaussiano e circular, mostrando que sob um adequado reescalamento elas são idênticas. Outros ensembles nesta dissertação foram investigados usando o Método de Gram para o caso em que os autovalores são limitados em um intervalo. Computamos a densidade de estados para cada um desses ensembles. Mais precisamente no ensemble de Chebychev, os resultados foram obtidos analiticamente e nesse ensemble além da densidade de estados, também traçamos grá…cos da função de correlação truncada. / In a detailed review we obtain a semi-circle law for the density of states in theWigner’s Gaussian Ensemble. Also we talk about Dyson’s Analogy, seeing the eigenvalues like charges that repulse themselves in the unitary circle, showing that this case the density of states is uniform. In a more general context we obtain the semi-circle law, proving the Glivenko-Cantelli Theorem to strongly correlated variables, using a combinatorial method of Paths' Counting. Thus we are showing the stability of the semi-circle Law. Also, in this dissertation we study the correlation functions in the Gaussian and Circular ensembles showing that using the Gram's Method in the case that eigenvalues are limited in a interval. In these ensembles we computed the density of states. More precisely, in a Chebychev ensemble the results were obtained analytically. In this ensemble, we also obtain graphics of the truncated correlation function.

Em uma detalhada revisão nós obtemos a lei do semi-círculo para a densidade de estados no ensemble gaussiano de Wigner. Também falamos sobre a analogia eletrostática de Dyson, enxergando os autovalores como cargas que se repelem no círculo unitário, mostrando que nesse caso a densidade de estados é uniforme. Em um contexto mais geral nós obtemos a lei do semicírculo, provando o teorema de Glivenko-Cantelli para variáveis fortemente correlacionadas usando um método combinatorial de contagem de trajetos, o que nos dá subsídios para falar em estabilidade da lei do semi-círculo. Também, nesta dissertação nós estudamos as funções de correlação nos ensembles gaussiano e circular, mostrando que sob um adequado reescalamento elas são idênticas. Outros ensembles nesta dissertação foram investigados usando o Método de Gram para o caso em que os autovalores são limitados em um intervalo. Computamos a densidade de estados para cada um desses ensembles. Mais precisamente no ensemble de Chebychev, os resultados foram obtidos analiticamente e nesse ensemble além da densidade de estados, também traçamos grá…cos da função de correlação truncada. / In a detailed review we obtain a semi-circle law for the density of states in theWigner’s Gaussian Ensemble. Also we talk about Dyson’s Analogy, seeing the eigenvalues like charges that repulse themselves in the unitary circle, showing that this case the density of states is uniform. In a more general context we obtain the semi-circle law, proving the Glivenko-Cantelli Theorem to strongly correlated variables, using a combinatorial method of Paths' Counting. Thus we are showing the stability of the semi-circle Law. Also, in this dissertation we study the correlation functions in the Gaussian and Circular ensembles showing that using the Gram's Method in the case that eigenvalues are limited in a interval. In these ensembles we computed the density of states. More precisely, in a Chebychev ensemble the results were obtained analytically. In this ensemble, we also obtain graphics of the truncated correlation function.

We have studied fundamental aspects of time-resolved two-photon excited fluorescence depolarisation. The thesis presents experimental as well as theoretical progress. We show that a multi-photon induced instrumental response function obtained from a suspension of gold nanoparticles is appropriate for the analysis of two-photon excited fluorescence decays obtained using time-correlated single photon counting detection. Theoretical expressions have been derived for the fluorescence anisotropy decay obtained upon two-photon excitation of various molecular systems in liquid solutions: a) an anisotropic rigid rotor that undergoes rotational diffusion in the presence of ultrafast unresolved restricted reorientations, e.g. librations. b) a molecular group covalently attached to a stationary macromolecule, and undergoing local reorientation in a uniaxial ordering potential. A new approach to the analysis of two-photon excited fluorescence depolarisation experiments was developed, which combines data obtained by using linearly and circularly polarised excitation light, in a global manner. In the analysis, knowledge about unresolved reorientations was obtained from one-photon excitation studies of the corresponding systems. By means of this procedure it has been possible to obtain quantitative information about the molecular two-photon absorption tensor for perylene and two of its derivatives. Thereby the symmetry of the final excited and intermediate vibronic states could be assigned. The analysis reveals that the two-photon transition studied with the 800 nm laser exhibits mixed character. An important finding from the experiments was that the two-photon absorption tensor appears to be solvent dependent. Furthermore, the thesis presents the first theoretical treatment of two-photon excited donor-donor energy migration in the presence of molecular reorientation and which applies the extended Förster theory. Explicit expressions for molecules that belong to the point groups D2h, D2 and C2v are given. Preliminary experiments are finally also reported on a two-photon excited donor-donor energy migration system consisting of a bisanthryl-bisteroid.

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Made available in DSpace on 2014-10-09T12:42:05Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:04:50Z (GMT). No. of bitstreams: 0 / Tese (Doutoramento) / IPEN/T / Instituto de Pesquisas Energeticas e Nucleares - IPEN-CNEN/SP