Derivation of Mass Spectrum and Magnetic Moments from Current Conservation in RelativisticO(3, 2)andO(4, 2)Theories

It is shown that in the framework of the noncompact dynamical group theory, for every choice of the current operator in the representation space, the requirements of current conservation and universality of charge determine the relativistic mass spectrum. The most general currents linear in the algebra and linear in the momenta are investigated, and mass spectra of the form $m=C(j+\frac{1}{2})$ in $O(3, 2)$, and of the form $m=Cn$ or $m=Cn{(1+\frac{a}{n^2})}^{\frac{1}{2}}$ in $O(4, 2)$, are derived with positive magnetic moments and with form factors in agreement with experiment. The freedom in the choice of currents, minimal or nonminimal, is discussed and compared with that which exists in the usual Lagrangian field theory.