Mapping the Spinless Fermion-Boson Model onto a Luttinger Liquid Model

The spinless fermion-boson model in one-dimension is studied via the Bethe ansatz method. The eigenstates of the model Hamiltonian are established. Some long distance correlation functions are calculated based on the prediction of the conformal field theory. It is shown that the low energy physics of the present model is equivalent to that of a Luttinger liquid model.