A new integrable model of quantum field theory in the state space with indefinite metric

Abstract

The system of coupled nonlinear Schrödinger equations (NLS) with noncompact internal symmetry group U( p, q) is considered. It describes in the quasiclassical limit the system of two “coloured” Bose-gases with point-interaction. The structure of the transition matrix is studied via the spectral transform (ST) (inverse method). The Poisson brackets of the elements of this matrix and integrals of motion it generates are found. The theory under consideration may be put in the corresponding quantum field theory in the state vector space with indefinite metric. The so-called R matrix (Faddeev) and commutation relations for the transition matrix elements are also obtained, which implies the model to be investigated with the help of the quantum version of ST.