On the S-Matrix of the Faddeev-Reshetikhin Model

TL;DR

This paper investigates the diagonalization of the Hamiltonian in the Faddeev-Reshetikhin model, revealing a family of interactions with unitary S-matrices, including PT-symmetric non-Hermitian cases.

Contribution

It identifies the most general quartic Hamiltonian that can be diagonalized and explores PT-symmetric non-Hermitian Hamiltonians with unitary S-matrices.

Findings

The Hamiltonian includes the bosonic Thirring model.

A new model shares the same two-particle S-matrix as the Faddeev-Reshetikhin model.

A one-parameter family of PT-symmetric, non-Hermitian Hamiltonians with unitary S-matrices was found.

Abstract

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.