Summing Certainφ4Graphs Using Integral Equations

Abstract

It is shown that the problem of summing certain graph chains occurring in ${\phi }^4$ theory in which we have three (or four) particles in the intermediate state is reducible to an integral equation. For forward scattering and zero-mass field, this equation can be solved exactly using a method for solving the Bethe-Salpeter equation which has been recently suggested. As an example, the case of the truss-bridge diagrams is worked out in detail.