Weyl–van der Waerden formalism for helicity amplitudes of massive particles

The Weyl–van der Waerden spinor technique for calculating helicity amplitudes of massive and massless particles is presented in a form that is particularly well suited to a direct implementation in computer algebra. Moreover, we explain how to exploit discrete symmetries and how to avoid unphysical poles in amplitudes in practice. The efficiency of the formalism is demonstrated by giving explicit compact results for the helicity amplitudes of the processes $\gamma \overrightarrow{\gamma }f\overline{f},$ $f\overline{f}\to \gamma \gamma \gamma ,$ ${\mu }^{-}{\mu }^{+}\to f\overline{f}\gamma .$