dorsal/arxiv
View SchemaSolvability of the G_2 Integrable System
| Authors | Marcos Rosenbaum, Alexander Turbiner, Antonio Capella |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9707005 |
| URL | https://arxiv.org/abs/solv-int/9707005 |
| DOI | 10.1142/S0217751X98001815 |
| Journal | Int.J.Mod.Phys. A13 (1998) 3885-3904 |
Abstract
It is shown that the 3-body trigonometric G_2 integrable system is exactly-solvable. If the configuration space is parametrized by certain symmetric functions of the coordinates then, for arbitrary values of the coupling constants, the Hamiltonian can be expressed as a quadratic polynomial in the generators of some Lie algebra of differential operators in a finite-dimensional representation. Four infinite families of eigenstates, represented by polynomials, and the corresponding eigenvalues are described explicitly.
{
"annotation_id": "b3398537-aacf-4570-8783-ac2cc2842551",
"date_created": "2026-03-02T18:02:50.625000Z",
"date_modified": "2026-03-02T18:02:50.625000Z",
"file_hash": "7c137a2b62dd120b6431e9ff2fc14e88511d7dbe8197ff1ed8319b1de7f11c46",
"private": false,
"record": {
"abstract": "It is shown that the 3-body trigonometric G_2 integrable system is\nexactly-solvable. If the configuration space is parametrized by certain\nsymmetric functions of the coordinates then, for arbitrary values of the\ncoupling constants, the Hamiltonian can be expressed as a quadratic polynomial\nin the generators of some Lie algebra of differential operators in a\nfinite-dimensional representation. Four infinite families of eigenstates,\nrepresented by polynomials, and the corresponding eigenvalues are described\nexplicitly.",
"arxiv_id": "solv-int/9707005",
"authors": [
"Marcos Rosenbaum",
"Alexander Turbiner",
"Antonio Capella"
],
"categories": [
"solv-int",
"cond-mat",
"hep-th",
"nlin.SI"
],
"doi": "10.1142/S0217751X98001815",
"journal_ref": "Int.J.Mod.Phys. A13 (1998) 3885-3904",
"title": "Solvability of the G_2 Integrable System",
"url": "https://arxiv.org/abs/solv-int/9707005"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "634e49ae-cb0e-47c6-a833-978d16642493",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}