Vertex function in the theory of the weak interaction of leptons

The Edwards approximation is used to study the vertex function in the theory of the weak $V$–$A$ interaction of leptons with the $W$ boson. Edwards's linear integral equation for the sum of ladder-type diagrams is reduced to a boundary-value problem for a system of linear differential equations. The existence and uniqueness of the solution of this problem is proved and the higher approximation corrections are estimated. The principal correction for the renormatized vertex function is found to be of order $g_2\ln g_2$. The proof makes essential use of dispersion sum rules and some new Euclidean momenta sum rules for the vertex function are derived.