On the equivalence theorem for integrable systems

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 nonlinear 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.