Symmetry of the Relativistic Two-Body Bound State

Abstract

We show that in a relativistically covariant formulation of the two-body problem, the bound state spectrum is in agreement, up to relativistic corrections, with the non-relativistic bound-state spectrum. This solution is achieved by solving the problem with support of the wave functions in an O ( 2 , 1 ) invariant submanifold of the Minkowski spacetime. The O ( 3 , 1 ) invariance of the differential equation requires, however, that the solutions provide a representation of O ( 3 , 1 ) . Such solutions are obtained by means of the method of induced representations, providing a basic insight into the subject of the symmetries of relativistic dynamics.