Solutions of the Gaudin Equation and Gaudin Algebras

摘要

Three well-known solutions of the Gaudin equation are obtained under a set ofstandard assumptions. By relaxing one of these assumptions we introduce a classof mutually commuting Hamiltonians based on a different solution of the Gaudinequation. Application of the algebraic Bethe ansatz technique to diagonalizethese Hamiltonians reveals a new infinite dimensional complex Lie algebra.