On the S-Matrix of the Faddeev-Reshetikhin Model

The Faddeev-Reshetikhin model arises as a truncation of strings in AdS_5XS^5. Its two particle S-matrix should be obtained by diagonalizing its Hamiltonian. However this does not happen in a straightforward way. There is a Lorentz violating term in the Hamiltonian which prevents its plain diagonalization. We then find out the most general quartic Hamiltonian that can be diagonalized. It includes the bosonic Thirring model as well as another model which shares the same two particle S-matrix as the Faddeev-Reshetikhin model. We also find a one parameter family of interactions which lead to non-Hermitian Hamiltonians which have unitary S-matrices and are PT symmetric.