Simplifying Algebra in Feynman Graphs, Part I:Spinors

Abstract

We present a general formalism for simplifying manipulations of spin indices of massless and massive spinors and vectors in Feynman diagrams. The formalism is based on covariantly reducing the number of field components in the action in favor of chiral/self-dual fields. In this paper we concentrate on calculational simplifications involving fermions in gauge theories by eliminating half of the components of Dirac spinors. Some results are: (1) We find reference momenta for massless fermions analogous to those used for external gauge bosons. (2) Many of the known supersymmetry identities (tree and one-loop) are seen in a simple manner from the graphs. (3) Manipulations with external line factrs for massive fermions are unnecessary. (4) Some of the simplifications for nearly maximally helicity violating gluonic amplitudes are built into the Feynman rules.