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Fonctions tau de l'operateur de Dirac sur le cylindre

Abstract : The thesis is devoted to the study of an analog of the Riemann-Hilbert problem and monodromy preserving deformations for the solutions of the Dirac equation on the cylinder. The aim is to understand the connection between deformation theory and correlation functions of certain integrable models of quantum field theory in the finite volume. In the first part, we study multivalued solutions of the Dirac equation that realize a unitary one-dimensional representation of the fundamental group of the cylinder with n marked points. We introduce and investigate the canonical basis of solutions, the Green function and the tau function of the singular Dirac operator. In the second part, we derive in two different ways nonlinear differential equations, satisfied by the correlation functions of the Ising model on the cylinder.
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Contributor : Oleg Lisovyy <>
Submitted on : Friday, January 7, 2005 - 2:03:16 PM
Last modification on : Thursday, March 5, 2020 - 12:06:06 PM
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  • HAL Id : tel-00007956, version 1


Oleg Lisovyy. Fonctions tau de l'operateur de Dirac sur le cylindre. Physique mathématique [math-ph]. Université d'Angers, 2004. Français. ⟨tel-00007956⟩



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