منابع مشابه
1 + 1 Gaudin Model
We study 1+1 field-generalizations of the rational and elliptic Gaudin models. For sl(N) case we introduce equations of motion and L-A pair with spectral parameter on the Riemann sphere and elliptic curve. In sl(2) case we study the equations in detail and find the corresponding Hamiltonian densities. The n-site model describes n interacting Landau– Lifshitz models of magnets. The interaction d...
متن کامل5 Gaudin model and opers
This is a review of our previous works [FFR, F1, F3] (some of them joint with B. Feigin and N. Reshetikhin) on the Gaudin model and opers. We define a commutative subalgebra in the tensor power of the universal enveloping algebra of a simple Lie algebra g. This algebra includes the hamiltonians of the Gaudin model, hence we call it the Gaudin algebra. It is constructed as a quotient of the cent...
متن کاملZn elliptic Gaudin model with open boundaries
The Zn elliptic Gaudin model with integrable boundaries specified by generic nondiagonal K-matrices with n+ 1 free boundary parameters is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding Bethe ansatz equations are obtained. PACS: 03.65.Fd; 04.20.Jb; 05.30.-d; 75.10.Jm
متن کاملAlgebraic Bethe Ansatz for XYZ Gaudin model
The eigenvectors of the Hamiltionians of the XYZ Gaudin model are constructed by means of the algebraic Bethe Ansatz. The construction is is based on the quasi-classical limit of the corresponding results for the inhomogeneous higher spin eight vertex model. EKS acknowledges the support of the Department of Mathematical Sciences, the University of Tokyo, where the most part of the work was done...
متن کاملSolutions of the Gaudin Equation and Gaudin Algebras
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.
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ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2011
ISSN: 1815-0659
DOI: 10.3842/sigma.2011.067