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Current issue   Ukr. J. Phys. 2014, Vol. 58, N 11, p.1084-1091
doi:10.15407/ujpe58.11.1084    Paper

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: yulia.bezvershenko@gmail.com)
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.