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In this thesis we investigate the quantum integrability of the Alday-Arutyunov-Frolov model (AAF) by diagonalization of the Hamiltonian of the AAF transformed model. The AAF transformed model is obtained from original model after fields redefinition whose purpose is to transform the Dirac brackets in the standard canonical structure between two fermions. For the diagonalization of the Hamiltonian of the transformed model we use the method developed for the Landau-Lifshitz model. This method requires regularization of the singular product of operators at the same point as well as construction of the selfadjoint extensions. We show that the wave function and the states of the transformed AAF exhibit discontinuities. We also investigated the equivalence of the matrices S of the two formulations of the AAF model through direct calculation of the S-matrix in both theories. We also consider the equivalence theorem applied to AAF model. To shows that the S matrix is invariant under field redefinitions.

Integrabilidade quântica do modelo de Alday-Arutyunov-Frolov