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Norm formulae for the Bethe Ansatz on root systems of small rank
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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. ISSN 17518113
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Official URL: http://dx.doi.org/10.1088/17518113/41/2/025202
Abstract
The norms of the Bethe Ansatz eigenfunctions for the LiebLiniger 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 GaudinKorepin 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 > Mathematics  
Library of Congress Subject Headings (LCSH):  Betheansatz technique, Root systems (Algebra), Eigenfunctions  
Journal or Publication Title:  Journal of Physics A: Mathematical and Theoretical  
Publisher:  IOP Publishing Ltd  
ISSN:  17518113  
Official Date:  18 January 2008  
Dates: 


Volume:  Volume 41  
Number:  Number 2  
Number of Pages:  13  
Page Range:  Article No. 025202  
Identification Number:  10.1088/17518113/41/2/025202  
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)  
References:  [B] Bourbaki N 1968 Groupes et alg`ebres de Lie (Paris: Hermann) chapitres 4–6 

URI:  http://wrap.warwick.ac.uk/id/eprint/30623 
Data sourced from Thomson Reuters' Web of Knowledge
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