Extended State Space of the Rational sl(2) Gaudin Model in Terms of Laguerre Polynomials
Keywords:Gaudin model, sl(2) representation theory, Laguerre polynomials
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.
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