Bustamante, Miguel D., Van Diejen, Jan Felipe and de la Maza, A. C. (2008) Norm formulae for the Bethe Ansatz on root systems of small rank. Journal of Physics A: Mathematical and Theoretical, Volume 41 (Number 2). Article No. 025202. doi:10.1088/1751-8113/41/2/025202 ISSN 1751-8113.
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Abstract
The norms of the Bethe Ansatz eigenfunctions for the Lieb-Liniger quantum system of n Bosonic particles on a ring with pairwise repulsive delta potential interactions are given by a beautiful determinantal formula, first conjectured by Gaudin in the early seventies and then proven by Korepin about a decade later. Recently, E Emsiz formulated a similar conjecture generalizing the Gaudin-Korepin norm formula in terms of the root systems of complex simple Lie algebras. Here we confirm the validity of the conjecture in question for small root systems up to rank 3 ( thus including the important test case of the exceptional root system G(2)).
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics |
| Library of Congress Subject Headings (LCSH): | Bethe-ansatz technique, Root systems (Algebra), Eigenfunctions |
| Journal or Publication Title: | Journal of Physics A: Mathematical and Theoretical |
| Publisher: | IOP Publishing Ltd |
| ISSN: | 1751-8113 |
| Official Date: | 18 January 2008 |
| Dates: | Date Event 18 January 2008 Published |
| Volume: | Volume 41 |
| Number: | Number 2 |
| Number of Pages: | 13 |
| Page Range: | Article No. 025202 |
| DOI: | 10.1088/1751-8113/41/2/025202 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| Funder: | Fondo Nacional de Desarrollo Científico y Tecnológico (Chile) (FONDECYT), World Bank, Universidad de Talca |
| Grant number: | 1051012, 1040896 (FONDECYT) |
| URI: | https://wrap.warwick.ac.uk/30623/ |
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