Four-Vectors and Helicity Amplitudes in πN Elastic Scattering

There is a natural way to introduce a set of four orthogonal four-vectors in the elastic scattering process. In the $\ensuremath{\pi}N$ elastic problem, they provide a covariant description of the helicity-flip and -nonflip processes. The nonflip interaction operator becomes a rotation through the scattering angle $\ensuremath{\theta}$ about the normal to the scattering plane; the helicity-flip interaction involves a rotation through $\ensuremath{\pi}+\ensuremath{\theta}$.