Solutions of the Gaudin Equation and Gaudin Algebras
A.B. Balantekin (Wisconsin U., Madison), T. Dereli (Koc U.), Y., Pehlivan (Izmir Inst. Tech.)
TL;DR
This paper explores solutions to the Gaudin equation, introduces a new class of commuting Hamiltonians by relaxing assumptions, and uncovers a novel infinite-dimensional Lie algebra through algebraic Bethe ansatz.
Contribution
It presents a new class of solutions to the Gaudin equation and identifies a previously unknown infinite-dimensional Lie algebra.
Findings
Three known solutions of the Gaudin equation are derived.
A new class of mutually commuting Hamiltonians is introduced.
A new infinite-dimensional complex Lie algebra is discovered.
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.
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