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## Main Question or Discussion Point

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)

Many thanks in advance for any help!

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!