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Séparation des variables et facteurs de forme des modèles intégrables quantiques

Abstract : 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.
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Submitted on : Tuesday, August 27, 2013 - 9:37:11 AM
Last modification on : Wednesday, November 20, 2019 - 2:46:28 AM
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  • HAL Id : tel-00854395, version 1


Nicolas Grosjean. Séparation des variables et facteurs de forme des modèles intégrables quantiques. Autre [cond-mat.other]. Ecole normale supérieure de lyon - ENS LYON, 2013. Français. ⟨NNT : 2013ENSL0816⟩. ⟨tel-00854395⟩



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