0372-400Х (Edition in Ukrainian)
2071-0186 (Edition in English)
2071-0194 (in electronic form)
Abbreviated key title: Ukr. J. Phys.
Bezvershenko Yu.V.1,2, Holod P.I.2
1 Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
(14b, Metrolohichna Str., Kyiv 03143, Ukraine; e-mail: firstname.lastname@example.org)
2 Faculty of Physical and Mathematical Sciences, National University of Kyiv-Mohyla Academy
(2, Skovorody Str., Kyiv 04070, Ukraine)
Extended State Space of the Rational sl(2) Gaudin Model in Terms of Laguerre Polynomials
Section: International Conference “Quantum Groups and Quantum Integrable Systems” Kyiv, June 18–21, 2013
Original Author's Text: English
Abstract: We consider the rational Gaudin model with non-zero magnetic field, which physically corresponds to the central spin problem. The space of states is described in terms of separated variables. The states of a spin system are given by rational (up to an exponential factor) functions of these variables on the Lagrangian submanifold. We build a representation of the sl(2) algebra of the model in terms of Laguerre polynomials and formulate the functional Bethe ansatz using it.
Key words: Gaudin model, sl(2) representation theory, Laguerre polynomials.