Quantization of the Gaudin System

2004/04/21 by D. Talalaev, Talalaev, D. · 1 citation
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #hep-th #math.QA #nlin.SI

paper · pdf · doi:10.48550/arxiv.hep-th/0404153

9 pages

arxiv created 2004/04/21 · arxiv updated 2009/12/01

Abstract

In this article we exploit the known commutative family in Y(gl(n)) - the Bethe subalgebra - and its special limit to construct quantization of the Gaudin integrable system. We give explicit expressions for quantum hamiltonians QI_k(u), k=1,..., n. At small order k=1,...,3 they coincide with the quasiclassic ones, even in the case k=4 we obtain quantum correction.

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• Bethe algebras for unitarizable modules over classical Lie (super)algebras and a duality

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