so(4) is the symmetry algebra of Keplerian motion. Its structure is well known. The principal quantum number n must be a positive integer. The associated Casimir operator has eingenvalues n^2 - 1 . The secondary quantum number j is integer and can take any value from zero to n-1. The eigenvalue of the "angular momentum squared" operator J^2 is j(j+1). Here my question: How is this for so(2,2) over the field of real numbers? Which values can the principal and the secondary quantum numbers take and which are the eigenvalues of the associated operators (Casimir operator; operator corresponding to J^2)? Many thanks in advance for any help!