Calculation of Relativistic Transition Probabilities and Form Factors from Noncompact Groups

Relativistic transition probabilities and form factors have been evaluated in closed form (in terms of hypergeometric functions) for a model of fundamental particles constructed on the unitary irreducible representation space of a noncompact dynamical group. Majorana-type equations have been used to project out irreducible subspaces of the Poincaré group and to specify the transformation properties of the electromagnetic current. The magnetic moment of the spin-½ ground state in the simplest representation is -½, and one obtains the observed symmetry $G_E\mathrm{}\left(t\right)=\frac{G_M\mathrm{}\left(t\right)\mathrm{}}{\mu }$.