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 $2(2j+1)$-component formalism. The propagators involve matrices which transform like symmetric traceless tensors of rank $2j$; they are the natural generalizations of the 2\ifmmode\times\else\texttimes\fi{}2 four-vector ${\ensuremath{\sigma}}^{\ensuremath{\mu}}$ and 4\ifmmode\times\else\texttimes\fi{}4 four-vector ${\ensuremath{\gamma}}^{\ensuremath{\mu}}$ 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 $P$.