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+1)component formalism [with fields of the (j, 0) or (0, j) type] or the 2(2j+1)component formalism [with (j, 0)⊕(0, j) fields]. But there are other field types which cannot be constructed for m=0; these include the (j2, j2) tensor fields, and in particular the vector potential for j=1. This restriction arises from the nonsemisimple 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.
 Publication:

Physical Review
 Pub Date:
 May 1964
 DOI:
 10.1103/PhysRev.134.B882
 Bibcode:
 1964PhRv..134..882W