nLab Toda lattice

Overview

Toda lattice is a particular completely integrable system, a model of a 1-dimensional crystal. It can be generalized to general root systems.

Relation to other models

Toda lattice can be obtained by reduction from Wess-Zumino models.

Literature

• wikipedia: Toda lattice
• Morikazu Toda, Vibration of a chain with a non-linear interaction“, J. Phys. Soc. Jpn., 22 (2) (1967) 431-436 doi
• Bertram Kostant, The solution to a generalized Toda lattice and representation theory, Adv. Math. 34, 195–338 (1998) pdf
• L. O’Raifeartaigh, V. V. Sreedhar, Path integral formulation of the conformal Wess-Zumino-Witten $\to$ Toda reductions, Nuclear Physics B 529:3 (1998) 547-566 doi