Physics – Mathematical Physics
Scientific paper
2012-02-09
Journal of Physics A:Math. Theor. 44, 445302 (2011)
Physics
Mathematical Physics
11 pages, 4 figures
Scientific paper
10.1088/1751-8113/44/44/445302
The "curved" Coulomb potential on the S3 ball, whose isometry group is SO(4), takes the form of a cotangent function, and when added to the four-dimensional squared angular momentum operator, one of the so(4) Casimir invariants, a Hamiltonian is obtained which describes a perturbance of the free geodesic motion that results peculiar in several aspects. The spectrum of such a motion has been studied on various occasions and is known to carry unexpectedly so(4) degeneracy patterns despite the non-commutativity of the perturbance with the Casimir operator. We here suggest an explanation for this behavior in designing a set of operators which close the so(4) algebra and whose Casimir invariant coincides with the Hamiltonian of the perturbed motion at the level of the eigenvalue problem. The above operators are related to the canonical geometric SO(4) generators on S3 by a non-unitary similarity transformation of the scaling type. In this fashion, we identify a complementary option to the deformed dynamical so(4) Higgs algebra constructed in terms of the components of the ordinary angular momentum and a related Runge-Lenz vector.
Kirchbach Mariana
Rivera Adrian Pallares
No associations
LandOfFree
Symmetry and degeneracy of the curved Coulomb potential on the S3 ball does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Symmetry and degeneracy of the curved Coulomb potential on the S3 ball, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Symmetry and degeneracy of the curved Coulomb potential on the S3 ball will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-157502