Adrian Pallares Rivera, Mariana Kirchbach
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.
View original:
http://arxiv.org/abs/1202.2021
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