Abstract
We find that there is a Yangian symmetry, i.e., Y(su(2)), in the model of a charged particle on the surface of a sphere with a magnetic monopole situating at the center. We construct generators of Y(su(2)) algebra explicitly and derive energy spectrum by employing its representation theory. We also show that this model is integrable from RTT relation.
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Notes
The conventions of irreducible representation for su(2) algebra we applied are different from the ones we are familiar with. The dimension of the irreducible representation is \(m+1\) with basis \(\{e_0, e_1, . . . , e_m \}\). The action of generators \((I_\pm , \ I_3)\) on this basis is \(I_+ e_i =(i+1) e_{i+1}, \ I_- e_i = (m-i +1) e_{i-1}, \ I_3 e_i \frac{1}{2}(2i -m) e_i\). The relation between this set of basis and the one we are familiar with was given in [20].
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Sun, EX., Ma, LB., Yuan, ZG. et al. Y(su(2)) Symmetry of Landau Levels on the Sphere. Int J Theor Phys 62, 133 (2023). https://doi.org/10.1007/s10773-023-05387-9
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DOI: https://doi.org/10.1007/s10773-023-05387-9