Abstract
We study classical and quantum hidden symmetries of a particle with electric charge e in the background of a Dirac monopole of magnetic charge g subjected to an additional central potential V (r) = U (r) + (eg)2/2mr2 with U (r) = \( \frac{1}{2} \)mω2r2, similar to that in the one-dimensional conformal mechanics model of de Alfaro, Fubini and Furlan (AFF). By means of a non-unitary conformal bridge transformation, we establish a relation of the quantum states and of all symmetries of the system with those of the system without harmonic trap, U (r) = 0. Introducing spin degrees of freedom via a very special spin-orbit coupling, we construct the \( \mathfrak{sop} \)(2|2) superconformal extension of the system with unbroken \( \mathcal{N} \) = 2 Poincaré supersymmetry and show that two different superconformal extensions of the one-dimensional AFF model with unbroken and spontaneously broken supersymmetry have a common origin. We also show a universal relationship between the dynamics of a Euclidean particle in an arbitrary central potential U (r) and the dynamics of a charged particle in a monopole background subjected to the potential V (r).
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Inzunza, L., Plyushchay, M.S. & Wipf, A. Hidden symmetry and (super)conformal mechanics in a monopole background. J. High Energ. Phys. 2020, 28 (2020). https://doi.org/10.1007/JHEP04(2020)028
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DOI: https://doi.org/10.1007/JHEP04(2020)028