Functional Integral Method In One-Dimensional Quantum Sine-Gordon-Thirring Model

The statistical physical properties of one-dimensional nonlinear quantum field model are investigated in this thesis. Two methods are introduced to study this kind of model. Bethe ansatz method can give exact physical results, but it applies only for limited classes of nonlinear models. Functional integration method can be applied to any of nonlinear systems, the actual evaluation depends on the perturbation theory. In this thesis, the statistical physical properties of 1D quantum sine-Gordon-Thirring model are studied by means of new functional integral method.This thesis mainly deals with two problems:1. The effective potential and free energy of sine-Gordon-Thirring model are derived by using perturbation functional integration method. Moreover, four-order statistical averages of two-impurity with condensed term are calculated in weak-coupling case.2. We will combine functional integrals and variational-cumulant expansion methods. The effective potential and free energy of sine-Gordon-Thirring model are derived by using new non-perturbation integration method. In addition, two-order statistical averages two-impurity with condensed term are calculated in strong-coupling case. The new works of this thesis are as follows:1. The effective potential and free energy of sine-Gordon-Thirring model are derived by means of perturbation functional integration and auxiliary Bose field methods, four-order statistical averages of two-impurity with condensed term are calculated in weak-coupling range.2. The effective potential and free energy of sine-Gordon-Thirring model are derived by means of new non-perturbation functional integration method, two variational parameters are introduced to calculate two-order statistical averages of two-impurity with condensed term in strong-coupling range.