Eigenvectors for the Partial-Wave "Crossing Matrices"

Let $a$, $b$, $c$, $d$ be spinless particles of equal mass, and consider the process $a+b\to c+d$. It was shown else-where that the crossing symmetry of the scattering amplitude for such a process implies an infinite number of finite-dimensional "crossing relations" for the associated partial waves. In this paper, we derive explicit expressions for complete orthogonal and biorthogonal sets of eigenvectors of the partial-wave crossing matrices. The general form of a partial wave which is consistent with crossing symmetry is thus determined.