2000/10/21 by I. Krichever, K. L. Vaninsky
Physics and Astronomy · #hep-th
published as Mirror Symmetry IV, AMS/IP. vol 33, 139-158 (2002) · 23 pages, Latex
arxiv created 2000/10/21 · arxiv updated 2009/11/30
We develop algebro-geometrical approach for the open Toda lattice. For a finite Jacobi matrix we introduce a singular reducible Riemann surface and associated Baker-Akhiezer functions. We provide new explicit solution of inverse spectral problem for a finite Jacoby matrix. For the Toda lattice equations we obtain the explicit form of the equations of motion, the symplectic structure and Darboux coordinates. We develop similar approach for 2D open Toda. Explaining some the machinery we also make contact with the periodic case.