Nonrelativistic factorizable scattering theory and the Calogero-Sutherland model

Abstract

We solve the SU(N)-invariant Yang-Baxter equations imposing only the unitarity condition. The usual S matrices should satisfy the crossing symmetry which originates from the CPT invariance of relativistic quantum-field theory. In this paper, we consider nonrelativistic SU(N)-invariant factorizable S matrices by relaxing the crossing symmetry and making the amplitudes for creating and annihilating new particles vanish and find that these S matrices are exactly the same as those of the multicomponent Calogero-Sutherland model, the quantum-mechanical model with the hyperbolic potential between particles and antiparticles. This particular solution is of interest since it cannot be obtained as a nonrelativistic limit of any known relativistic solutions of the SU(N)-invariant Yang-Baxter equations.