Supercovergent sum-rules and the electromagnetic form-factors of elementary particles

The covarient formalism of Scadron et. al. is extended to cover processes involving virtual photons, and is used to discuss the 0(3,1)⨂SU(2) decomposition into kinematic singularity free form-factors of hadron-virtual photon three and four-point functions. An S-matrix theory of inelastic hadronlepton electromagnetic scattering is employed to develop techniques whereby superconvergent sum-rules on such four-point functions may be derived. Attention is focused on the virtual photoproduction off nucleons of non-strange pseudoscalar and vector mesons with isospin zero or unity. Charge-conjugation invarience of hadronvirtual photon interactions is assumed and eighty new sum-rules obtained. An alternative set of new sum-rules is derived on the assumption that such interactions are not in fact charge-conjugation invarient. A finite, width resonance approximation is used in an attempt to saturate the sum-rules for pion and ɳ production. This yields a large number of predictions concerning the structure of the form-factors parameterising the electromagnetic excitation of the nucleon into the ∆ (1236), N(1525), N(1550), N(1680), and N(1688). The sum-rules and predictions are valid for all non time-like values of the squared four-momentum of the virtual photon. The predictions are in good agreement with the experimental data in cases where a comparison has proved possible.