Feynman Rules for Any Spin

The explicit Feynman rules are given for massive particles of any spin j, in both a $2j+1$-component and a $2(2j+1)$-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=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.