Hidden symmetry and (super)conformal mechanics in a monopole background

• URL: http://arxiv.org/abs/2002.04341v4
• Date: Thu, 9 Apr 2020 01:59:05 GMT
• Title: Hidden symmetry and (super)conformal mechanics in a monopole background
• Authors: Luis Inzunza, Mikhail S. Plyushchay, Andreas Wipf
• Abstract summary: 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 $U(r)=tfrac12momega2r2$. 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
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $V(r)=U(r) +(eg)^2/2mr^{2}$ with $U(r)=\tfrac{1}{2}m\omega^2r^2$, 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 $\mathfrak{osp}(2,2)$ superconformal extension of the system with unbroken $\mathcal{N}=2$ Poincar\'e 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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