Generalized mass-scattering integrals for Dirac fields and their graphical representation

Abstract

Penrose suggested that Dirac fields could be constructed from an infinite number of elementary distributional fields scattering off each other, with the mass of the entire fields playing the role of a coupling constant. Following this suggestion, we present a complete null description of the mass-scattering processes. The general pattern of the null initial data for successive processes is explicitly exhibited. The entire fields are given by four series of terms, each being a manifestly finite scaling-invariant integral which is taken over a compact space of appropriate mass-scattering zigzags. A set of simple rules which enable one to evaluate any term of the series in a graphical way is given. These rules give rise to a colored-graph representation of the scattering integrals.