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Solutions of the Gaudin equation and Gaudin algebras

A B Balantekin1, T Dereli2 and Y Pehlivan3

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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.


PACS

03.65.Fd Algebraic methods

02.20.Sv Lie algebras of Lie groups

02.10.-v Logic, set theory, and algebra

MSC

22E65 Infinite-dimensional Lie groups and their Lie algebras (See also 17B65, 58B25, 58H05)

82B23 Exactly solvable models; Bethe ansatz

37K30 Relations with infinite-dimensional Lie algebras and other algebraic structures

Subjects

Mathematical physics

Quantum information and quantum mechanics

Dates

Issue 25 (24 June 2005)

Received 12 April 2005

Published 8 June 2005



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