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.
- Bound states
- Covariant two-body central force problem
- Relativistic quantum mechanics