论文标题
隐藏的对称性和（超级）在单极背景中
Hidden symmetry and (super)conformal mechanics in a monopole background
论文作者
论文摘要
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 $U(r)=\tfrac{1}{2}mω^2r^2$, similar to that in the one-dimensional conformal mechanics De Alfaro，Fubini和Furlan（AFF）的模型。通过非统一的共形桥变换，我们建立了量子状态的关系以及系统的所有对称性与无谐波陷阱的系统的关系，$ u（r）= 0 $。我们通过非常特殊的自旋轨道耦合引入自旋程度的自由度，我们构建了$ \ mathfrak {osp}（2,2）（2,2）$与不间断的$ \ mathcal {n} = 2 $poincaréSupersymmetrymetry，并显示了两种不同的超级共同范围的超级范围的超级范围的超级传统，并与模型不合时宜地散布了模型 起源。我们还显示了任意中央电势$ u（r）$中欧几里得粒子的动力学与受电势背景中的带电粒子的动力学之间的普遍关系。
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 $U(r)=\tfrac{1}{2}mω^2r^2$, 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 $\mathcal{N}=2$ 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 $V(r)$.
