The general kinematic properties of vertex functions which follow from the transformation properties of the initial and final single-particle states, and of the vertex (current) operator under proper and improper Lorentz transformations, are studied for the pseudoscalar (pion) and vector (electromagnetic) vertices. The treatment, which relies strongly on the helicity representation for the states of a relativistic particle introduced by Jacob and Wick, is fully relativistic, and applies to particles of arbitrary spin. The number of independent vertex functions or form factors is determined in each case, and the analogs of the nonrelativistic multipole expansions are obtained. One obtains thereby a complete specification of the dependence of the matrix elements on the spins, helicities, and relative parities of the particles, and some information on the limiting behavior of the form factors for small momentum transfers. A theorem first proved by Ernst, Sachs, and Wali in the special case of spin J, that the matrix elements of the 4-divergence of the electromagnetic current between states of the same (single) particle vanish independently of the assumption of gauge invariance or current conservation, is extended as a byproduct of the general results to the case of arbitrary spin and to any vector current having the same transformation properties as y M . Finally, the parametrizations obtained for the pseudoscalar and vector vertex functions are used to calculate the cross sections for the general two-particle scattering process a-\-b -> c-\-d in the single-quantum-exchange approximation for relativistic particles of arbitrary spin.

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A model for elastic scattering near the 900-MeV iT-p resonance is proposed, consisting of a Breit-Wigner term together with an optical background. The optical background is chosen to fit experimental data beyond the 900-MeV resonance; the spin of the Breit-Wigner term is then adjusted to give an elastic cross section in agreement with experiment. A distorted-wave Born-approximation calculation shows a spin-f resonance term to be in agreement with the data, in accord with the usual spin assignment. Parity of the Breit-Wigner term cannot be decided from the elastic energy spectra and angular distributions alone; however, if the elastic resonance is identified with the observed K-K resonance near 900 MeV, one finds a suitable branching ratio only for the Z) 5 / 2 choice. The resulting K-K angular distributions, as well as the production cross section as a function of energy, agree generally with experiment. It is therefore proposed that the 900-MeV w~-p resonance has negative parity relative to the proton.

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