Lagrangian Multiform for Cyclotomic Gaudin Models
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917838260797440 |
|---|---|
| author | Caudrelier, Vincent Singh, Anup Anand Vicedo, Benoît |
| author_facet | Caudrelier, Vincent Singh, Anup Anand Vicedo, Benoît |
| contents | We construct a Lagrangian multiform for the class of cyclotomic (rational) Gaudin models by formulating its hierarchy within the Lie dialgebra framework of Semenov-Tian-Shansky and by using the framework of Lagrangian multiforms on coadjoint orbits. This provides the first example of a Lagrangian multiform for an integrable hierarchy whose classical $r$-matrix is non-skew-symmetric and spectral parameter-dependent. As an important by-product of the construction, we obtain a Lagrangian multiform for the periodic Toda chain by choosing an appropriate realisation of the cyclotomic Gaudin Lax matrix. This fills a gap in the landscape of Toda models as only the open and infinite chains had been previously cast into the Lagrangian multiform framework. A slightly different choice of realisation produces the so-called discrete self-trapping (DST) model. We demonstrate the versatility of the framework by coupling the periodic Toda chain with the DST model and by obtaining a Lagrangian multiform for the corresponding integrable hierarchy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12837 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lagrangian Multiform for Cyclotomic Gaudin Models Caudrelier, Vincent Singh, Anup Anand Vicedo, Benoît Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems We construct a Lagrangian multiform for the class of cyclotomic (rational) Gaudin models by formulating its hierarchy within the Lie dialgebra framework of Semenov-Tian-Shansky and by using the framework of Lagrangian multiforms on coadjoint orbits. This provides the first example of a Lagrangian multiform for an integrable hierarchy whose classical $r$-matrix is non-skew-symmetric and spectral parameter-dependent. As an important by-product of the construction, we obtain a Lagrangian multiform for the periodic Toda chain by choosing an appropriate realisation of the cyclotomic Gaudin Lax matrix. This fills a gap in the landscape of Toda models as only the open and infinite chains had been previously cast into the Lagrangian multiform framework. A slightly different choice of realisation produces the so-called discrete self-trapping (DST) model. We demonstrate the versatility of the framework by coupling the periodic Toda chain with the DST model and by obtaining a Lagrangian multiform for the corresponding integrable hierarchy. |
| title | Lagrangian Multiform for Cyclotomic Gaudin Models |
| topic | Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2405.12837 |