Boost Operator and Its Application to Quantum Gelfand-Levitan Equation for Heisenberg-Ising Chain with Spin One-Half

Abstract

The quantum inverse scattering problem for the Ising-like XXZ model is studied. It is found that the boost operator plays an essential role in the analysis. In terms of the boost operator, the bound state operators are defined and the quantum Gelfand-Levitan equation is derived in a natural way. The quantum inverse scattering problem for the XY-like XXZ model is also discussed. In addition, the boost operators for Calogero systems and Toda lattice are explicitly given.