Numerical solution of the one-pair equation in the massive Schwinger model
The massive Schwinger model for fermions is considered which leads to an infinite set of coupled integral equations. To obtain a manageable set of equations the Fock-state expansion is truncated and this paper considers the most severe truncation applied to a meson-like state which reduces the system to one equation for one fermion-anti-fermion state. Various numerical methods are considered for the solution of this equation: (1) An expansion in terms of sine functions together with a judicious choice of collocation points. (2) The application of a standard Gauss-Chebyshev quadrature formula. (3) A finite element method. The results of using these methods are compared.
scientific article; zbMATH DE number 4102459