2005/10/31 by O. Babelon, Olivier Babelon
Engineering · Mathematics · Physics and Astronomy · #Bladed Disk Vibration Dynamics #Eigenvalues and eigenvectors #Lattice (music) #Limit (mathematics) #Mathematical and Theoretical Analysis #Poisson algebra #Poisson bracket #Poisson distribution #Scaling limit #Separation of variables #Statistical Mechanics and Entropy #hep-th
paper · pdf · doi:10.1007/s00220-006-0045-x
published as Commun.Math.Phys.266:819-862,2006 · Latex, 43 pages Synchronized with the to be published version
arxiv created 2006/03/21 · openalex publication_date 2006/06/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.