  We investigate the equivalence theorem for integrable systems using two
formulations of the Alday-Arutyunov-Frolov model. We show that the S-matrix is
invariant under the field transformation which reduces the non-linear Dirac
brackets of one formulation into the standard commutation relations in the
second formulation. We also explain how to perform the direct diagonalization
of the transformed Hamiltonian by constructing the states corresponding to
self-adjoint extensions.
