Properties And Numerical Approximation Of The Solution Ofthe Schwinger-Dyson Equation

Schwinger-Dyson (SD) equations provide us an important method of non-perturbation field theory. In this paper, after simplifying the ladder SD equation in Landau gauge, we study the existence and uniqueness of the solution of this equation. On above foundation, we discretize this nonlinear Hammerstein type integral equation to a nonlinear algebraic equation system, and prove under some hypotheses, the discrete solution converges to the continuous solution and the order of convergence is quadratic when the step converge to 0. Then, we can use simple iterative method to approximate the solution of the nonlinear algebraic equation system we obtain above. Besides, to improve the effect of approxima-tion, we also use Newton—Kantorovich (NK) method to approximate this solution. At last, we make program by MATLAB and compare the result with the analysis above.The whole thesis consists of five chapters. In the first chapter, we introduce the relative background and the main result. In chapter 2, we simplify the equation. In chapter 3, we approximate the solution of the simplified equation by simple iterative method. In chapter 4, we approximate the solution of the simplified equation by NK method. In chapter 5, we make program by MATLAB and compare the result with the analysis above.