Functional equation underlying the quantum theory of fields

Abstract

In the case of equality of vector and axial-vector couplings, useful to investigate the problem of mass generation for spinor fields by spontaneous symmetry breaking, all one-loop two-point Green's functions appear finite. The Mellin-transformed Schwinger-Dyson integral equations reduce to a finite-difference equation solved by a confluent hypergeometric function of the reduced kinematic variable. In this paper, the limiting process from the massive spinor to the massless case is treated in detail, all subsidiary terms being bounded and expressible in terms of Appell series and generalized confluent hypergeometric series.