Noncompact dynamical symmetry of a spin-orbit-coupled oscillator

作者：Haaker S M^*; Bais F A; Schoutens K

来源：Physical Review A, 2014, 89(3): 032105.

DOI：10.1103/PhysRevA.89.032105

We explain the finite as well as infinite degeneracy in the spectrum of a particular system of spin-1/2 fermions with spin-orbit coupling in three spatial dimensions. Starting from a generalized Runge-Lenz vector, we explicitly construct a complete set of symmetry operators, which span a noncompact SO(3,2) algebra. The degeneracy of the physical spectrum only involves an infinite, so-called singleton representation. In the branch where orbital and spin angular momentum are aligned, the full representation appears, constituting a three-dimensional analog of Landau levels. Antialigning the spin leads to a finite degeneracy due to a truncation of the singleton representation. We conclude the paper by constructing the spectrum generating algebra of the problem.

• 出版日期2014-3-5