Solutions of the Gaudin equation and Gaudin algebras
Abstract
Three well-known solutions of the Gaudin equation are obtained under a set of standard assumptions. By relaxing one of these assumptions, we introduce a class of mutually commuting Hamiltonians based on a different solution of the Gaudin equation. Application of the algebraic Bethe ansatz technique to diagonalize these Hamiltonians reveals a new infinite-dimensional complex Lie algebra.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- June 2005
- DOI:
- arXiv:
- arXiv:math-ph/0505071
- Bibcode:
- 2005JPhA...38.5697B
- Keywords:
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- pairing in many-body systems algebraic Bethe ansatz Gaudin algebras;
- Mathematical Physics;
- Condensed Matter - Strongly Correlated Electrons;
- Mathematics - Mathematical Physics;
- Nuclear Theory
- E-Print:
- 15 pages of LATEX