Relativistic Wave Equations for Particles with Internal Structure and Mass Spectrum

Abstract

We consider a class of wave equations which couple an infinite number of tensors or spinors of all ranks. Such a system of equations naturally possesses an infinite number of mass levels, and each eigenfunction implicitly contains a built-in form factor. Two simple examples of first order differential equations are examined. One is based on the set of all finite representations n(.y, -f-) or n(-f-+s, -f-) +D(-f-, -f-+s), n~O, 1, 2, , of the Lorentz group, and gives a mass spectrum resembling the hydrogen atom, but probability densities and form factors are unphysical. The other model is based on a unitary representation of the group 0(4, 2), and has an inverted hydrogen-like spectrum. The latter corresponds to a generalization of a model first proposed by Majorana.