Feynman Rules for Any Spin. III

Free fields, which transform according to general irreducible representations of the homogeneous Lorentz group, are constructed for any spin. The most general interactions may be built up from these fields, without explicit derivaties. The propagators for these fields are calculated in terms of previously calculated propagators for ($2j+1$)-component fields and Racah coefficients. A general formula is given which describes the decomposition of these propagators into various "daughter" spin exchanges.