Simultaneous partial wave expansion in the Mandelstam variables: the group SU(3)

The elastic scattering amplitude of two spinless particles of equal mass ½ was expanded elsewhere in a double series of eigenfunctions which 'displayed' its dependence on all the Mandelstam variables s, t, u (s+t+u=1). The expansion was then used to investigate the crossing properties of partial-wave amplitudes. We show in this paper that these eigenfunctions are certain basis vectors of the representations (s, s) of a suitably defined SU(3). The unequal-mass problem is also discussed.