Quantum Gelfand-Levitan equations for nonlinear Schrödinger model of spin-½ particles

Abstract

The quantum Gelfand-Levitan equations for the nonlinear Schr\"odinger model of spin-\textonehalf{} particles are obtained. Two Izergin-Korepin relations are used in the derivation. A new type commutation relation of $L$ operators is introduced to get the commutation relations which are needed for the study of $S$ matrices and Green's functions. As examples, the four-point Green's functions and the two-body $S$ matrices are given.