Feynman Rules for Any Spin

Abstract

The explicit Feynman rules are given for massive particles of any spin j, in both a 2j+1-component and a 2(2j+l)-component formalism. The propagators involve matrices which transform like symmetric traceless tensors of rank 2j; they are the natural generalizations of the 2×2 four-vector σ^µ and 4×4 four-vector γ^µ for $j\frac{1}{2}$. Our calculation uses field theory, but only as a convenient instrument for the construction of a Lorentz-invariant S matrix. This approach is also used to prove the spin-statistics theorem, crossing symmetry, and to discuss T, C, and P.

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.