Permutation Symmetries of Two-Body Amplitudes

Considerations of permutation symmetry among the three channels in two-body scattering suggest that only amplitudes of symmetry $S$ are nonvanishing in the forward direction at infinite energies; the other three-object symmetries $A$ and $D$ are not represented. For unlike scattering particles, this result is equivalent to an earlier one based on Pomeranchuk's theorem. For like particles the restrictions are much stronger and contradict the dominance of universal particle exchange at high energies; limiting cross sections will not generally be independent of isotopic spin, although this is accidentally true for $\mathrm{NN}$ scattering. Applications are here restricted mainly to isotopic spin, although an interesting point emerges: Particles with half-integer isotopic spin must also possess some other intrinsic parameter of spinor character.