Loop algebras, gauge invariants and a new completely integrable system
| dc.creator | Quinn, M. | |
| dc.creator | Singer, S. F. | |
| dc.date | 1996-06-25 | |
| dc.date.accessioned | 2026-07-07T09:17:53Z | |
| dc.date.available | 2026-07-07T09:17:53Z | |
| dc.description | One fruitful motivating principle of much research on the family of integrable systems known as ``Toda lattices'' has been the heuristic assumption that the periodic Toda lattice in an affine Lie algebra is directly analogous to the nonperiodic Toda lattice in a finite-dimensional Lie algebra. This paper shows that the analogy is not perfect. A discrepancy arises because the natural generalization of the structure theory of finite-dimensional simple Lie algebras is not the structure theory of loop algebras but the structure theory of affine Kac-Moody algebras. In this paper we use this natural generalization to construct the natural analog of the nonperiodic Toda lattice. Surprisingly, the result is not the periodic Toda lattice but a new completely integrable system on the periodic Toda lattice phase space. This integrable system is prescribed purely in terms of Lie-theoretic data. The commuting functions are precisely the gauge-invariant functions one obtains by viewing elements of the loop algebra as connections on a bundle over $S^1$. | |
| dc.identifier | https://arxiv.org/abs/solv-int/9606008 | |
| dc.identifier | http://arxiv.org/abs/solv-int/9606008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153830 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Loop algebras, gauge invariants and a new completely integrable system | |
| dc.type | text |