The S-matrix of the Faddeev-Reshetikhin model, diagonalisability and PT symmetry
Seminar Room 1, Newton Institute
We consider the diagonalizability of the Hamiltonian for the Faddeev-Reshetikhin (FR) model in the two particle sector. We find that the Hamiltonian is not diagonalizable. We then look for the most general quartic interaction Hamiltonian that can be diagonalized. This includes the bosonic Thirring model as well as the bosonic chiral Gross-Neveu model which we find share the same S-matrix. In addition, we find a general quartic interaction Hamiltonian, violating Lorentz invariance, that can be diagonalized with the same two particle S-matrix element as calculated by Klose and Zarembo for the FR model. This family of generalized interaction Hamiltonians is not Hermitian, but is PT symmetric, and belongs to a class of non-Hermitian but PT symmetric Hamiltonians which lead to a unitary S-matrix.
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