Infinite-Component Wave Equations with Hydrogenlike Mass Spectra

Continuing a previous work, various models of relativistic wave equations are considered which have an infinite number of components. By combining a unitary representation of $SO(4, 2)$ and the ordinary finite (Dirac) representation of the Lorentz group, it is possible to construct equations which produce hydrogenlike mass spectra. However, they are also accompanied by redundant, or unphysical, solutions. In the nonrelativistic limit, on the other hand, the equations obtained can be shown to be mathematically equivalent to the Schrödinger equation for the hydrogen atom. This suggests that the method of infinite-component wave equations may be a useful tool in exploring the physics of strong interactions. A general discussion is made about the principles and problems that will be relevant in pursuing such a program.