Continuum limit of the Volterra model, separation of variables and non standard realizations of the Virasoro Poisson bracket. - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Communications in Mathematical Physics Année : 2006

Continuum limit of the Volterra model, separation of variables and non standard realizations of the Virasoro Poisson bracket.

Résumé

The classical Volterra model, equipped with the Faddeev-Takhtadjan 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.
Fichier principal
Vignette du fichier
volterra.pdf (370.74 Ko) Télécharger le fichier

Dates et versions

hal-00012185 , version 1 (17-10-2005)
hal-00012185 , version 2 (21-03-2006)

Identifiants

Citer

Olivier Babelon. Continuum limit of the Volterra model, separation of variables and non standard realizations of the Virasoro Poisson bracket.. Communications in Mathematical Physics, 2006, 266, pp.819-862. ⟨10.1007/s00220-006-0045-x⟩. ⟨hal-00012185v2⟩
68 Consultations
113 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More