SO(4, 2)-Formulation of the Symmetry Breaking in Relativistic Kepler Problems with or without Magnetic Charges

Abstract

The relativistic Kepler problems in Dirac and Klein‐Gordon forms are solved by dynamical group methods for particles having both electric and magnetic charges (dyons). The explicit forms of the O(4, 2)‐algebra and two special O(2, 1)‐algebras (which coincide in the symmetry limit) are given, and a new group‐theoretical form of the symmetry breaking is pointed out. The Klein‐Gordon O(2, 1)‐algebra also solves the dynamics in the case of very strong coupling constants (attractive singular potential), if the principal series of representations is used instead of the discrete series.