Bethe–Salpeter Equation with Self–Energy Graphs I—Generalized Fredholm Theory, Parameter Imbedding Method11The project supported in part by National Natural Science Foundation of China.

Abstract

In this paper the classical Fredholm theory is generalized. The conceptions of the generalized fredholm denominator (GFD) and generalized Fredholm numerator (GFN) are defined. A set of parameter imbedding equations for GFD and GFN is deduced. In this way, the eigenvalue problem of the BS equation in ladder approximation with self–energy graphs, and the eigenvalue problem of nonlinear parameter integral equation, are carried over into an initial–value problem of a set of ordinary differential equations.