Feynman Rules for Any Spin. II. Massless Particles

Abstract

The Feynman rules are derived for massless particles of arbitrary spin j. The rules are the same as those presented in an earlier article for m>0, provided that we let m → 0 in propagators and wave functions, and provided that we keep to the (2j+l)-component formalism [with fields of the (j,0) or (0,j) type] or the 2(2j+l)-component formalism [with (j,0) ⊕ (0,J) fields]. But there are other field types which cannot be constructed for m = 0; these include the (j/2,j/2) tensor fields, and in particular the vector potential for j = 1. This restriction arises from the non-semi-simple structure of the little group for m = 0. Some other subjects discussed include: T, C, and P for massless particles and fields; the extent to which chirality conservation implies zero physical mass; and the Feynman rules for massive particles in the helicity formalism. Our approach is based on the assumption that the S matrix is Lorentz invariant, and makes no use of Lagrangians or the canonical formalism.

Research supported in part by the U. S. Air Force Office of Scientific Research, Grant No. AF-AFOSR-232-63.

Alfred P. Sloan Foundation Fellow.