Using The Improved Coordinate Bethe Ansatz Of Binning To Solve The Tonks-Girardeau Model

In the strongly coupled quantum field theory,the traditional perturbation method is no longer effective.The Coordinate Bethe Ansatz is a powerful tool for models with limited N particles,which becomes a continuum quantum field theory in the large N limit.However,as the N becomes larger,the amount of calculation also increases.We hope to simplify the calculation by the binning method.In the first chapter,we showed the background and motivation of this work,then we introduced the Coordinate Bethe Ansatz and the Tonks-Girardeau model briefly and gave the Coordinate Bethe Ansatz and the Bethe equations corresponding to the Tonks-Girardeau model.In the second chapter,we introduced the constant-density gas and gave its exact solution by some technics in number theory.In the third chapter,we then use the Coordinate Bethe Ansatz and the binning method to approximate the matrix elements corresponding to the constant-density gas,then we compared the results with the exact solution to show the effectivity of our binning method.In the last chapter we took a review of this work and gave the outlook.It is hoped that this method can be extended to the case of strongly coupled continuum quantum field theory.