Continuum Limit of the Volterra Model, Separation of Variables and Non-Standard Realizations of the Virasoro Poisson Bracket |
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Authors: | O Babelon |
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Institution: | (1) Laboratoire de Physique Théorique et Hautes Energies (LPTHE), Unité Mixte de Recherche (UMR 7589), Université Pierre et Marie Curie-Paris6; CNRS; Université Denis Diderot-Paris7, Tour 24-25, 5éme étage, Boite 126, 4 place Jussieu, 75252 Paris Cedex 05, France |
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Abstract: | The classical Volterra model, equipped with the Faddeev-Takhtajan Poisson bracket provides a lattice version of the Virasoro algebra. The Volterra model being integrable, we can express the dynamical variables in terms of the so-called separated variables. Taking the continuum limit of these formulae, we obtain the Virasoro generators written as determinants of infinite matrices, the elements of which are constructed with a set of points lying on an infinite genus Riemann surface. The coordinates of these points are separated variables for an infinite set of Poisson commuting quantities including L
0. The scaling limit of the eigenvector can also be calculated explicitly, so that the associated Schroedinger equation is in fact exactly solvable. |
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