I. Crossing transformations constitute a group of permutationsunder which the scattering amplitude is invariant. Using Mandelstem'sanalyticity, we decompose the amplitude into irreducible representationsof this group. The usual quantum numbers, such as isospin orSU(3), are "crossing-invariant". Thus no higher symmetry is generatedby crossing itself. However, elimination of certain quantum numbersin intermediate states is not crossing-invariant, and higher symmetrieshave to be introduced to make it possible. The currentliterature on exchange degeneracy is a manifestation of this statement.To exemplify application of our analysis, we show how, starting withSU(3) invariance, one can use crossing and the absence of exoticchannels to derive the quark-model picture of the tensor nonet. Nodetailed dynamical input is used.
II. A dispersion relation calculation of the real parts of forwardπ±p and K±p scattering amplitudes is carried out under the assumptionof constant total cross sections in the Serpukhov energy range.Comparison with existing experimental results as well as predictionsfor future high energy experiments are presented and discussed.Electromagnetic effects are found to be too small to account for theexpected difference between the π-p and π+p total cross sections athigher energies.
