Two examples of covariant theories with internal symmetries involving spin

Abstract

Although there are severe limitations on the combination of Poincaré group and an internal group it is shown in two examples how such a consistent combination can be achieved. The first example deals with the Bethe—Salpeter equation of two interacting scalar particles via a mass-zero scalar particle, and neglects consistently the spin-orbit coupling. The second example is the hydrogen atom where a non-compact group is used to describe all states of the system in the limit of energies being equal.