Adler-Kostant-Symes systems as Lagrangian gauge theories
Mathematical Physics
2015-06-26 v1 High Energy Physics - Theory
math.MP
Exactly Solvable and Integrable Systems
Abstract
It is well known that the integrable Hamiltonian systems defined by the Adler-Kostant-Symes construction correspond via Hamiltonian reduction to systems on cotangent bundles of Lie groups. Generalizing previous results on Toda systems, here a Lagrangian version of the reduction procedure is exhibited for those cases for which the underlying Lie algebra admits an invariant scalar product. This is achieved by constructing a Lagrangian with gauge symmetry in such a way that, by means of the Dirac algorithm, this Lagrangian reproduces the Adler-Kostant-Symes system whose Hamiltonian is the quadratic form associated with the scalar product on the Lie algebra.
Keywords
Cite
@article{arxiv.math-ph/0202033,
title = {Adler-Kostant-Symes systems as Lagrangian gauge theories},
author = {L. Feher and A. Gabor},
journal= {arXiv preprint arXiv:math-ph/0202033},
year = {2015}
}
Comments
10 pages, LaTeX2e