Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-10-18
Commun.Math.Phys.266:819-862,2006
Physics
High Energy Physics
High Energy Physics - Theory
Latex, 43 pages Synchronized with the to be published version
Scientific paper
10.1007/s00220-006-0045-x
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.
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