Relativistic transition amplitudes in a class of O(4,2) infinite multiplets. I. Continuum-continuum transitions

Abstract

A class of unitary irreducible O(4, 2) representations characterized by the lowest spin $\ensuremath{\mu}$, $\ensuremath{\mu}=0, \ifmmode\pm\else\textpm\fi{}\frac{1}{2}, \ifmmode\pm\else\textpm\fi{}1, \dots{}$, and the corresponding infinite-component wave equations are considered. The continuum-continuum transition amplitudes are evaluated by the method of analytic continuation generalizing the relativistic Coulomb case ($\ensuremath{\mu}=0$). A general exact Regge-type amplitude is derived, which contains the relativistic scattering amplitudes of O(4)-symmetric Coulomb interactions of two dyons in the symmetric model and amplitudes in certain hadron models as special cases.