标题： 五维开普勒系统中非中心势和杨-库仑单极相互作用的二次代数结构 显示英文标题

标题： Quadratic algebra structure in the 5D Kepler system with non-central potentials and Yang-Coulomb monopole interaction

摘要： 我们构建了在$su(2)$杨-库仑单极场中具有非中心势的5D变形开普勒系统的运动积分。 我们证明这些积分形成一个高阶二次代数$Q(3; L^{so(4)}, T^{su(2)})\oplus so(4)$，其结构常数涉及$so(4)$和$su(2)$李代数的Casimir算子。 我们通过变形振荡器实现该二次代数，并构造其有限维单位表示。 这使我们能够代数地推导出该系统的能量谱。 此外，我们证明该模型是多可分离的，并且可以在超球坐标和抛物线坐标中分离变量。 我们还证明其8D对偶系统（即8D奇异谐振子）在欧拉坐标和圆柱坐标中是可分离的。 显示英文摘要

摘要： We construct the integrals of motion for the 5D deformed Kepler system with non-central potentials in $su(2)$ Yang-Coulomb monopole field. We show that these integrals form a higher rank quadratic algebra $Q(3; L^{so(4)}, T^{su(2)})\oplus so(4)$, with structure constants involving the Casimir operators of $so(4)$ and $su(2)$ Lie algebras. We realize the quadratic algebra in terms of the deformed oscillator and construct its finite-dimensional unitary representations. This enable us to derive the energy spectrum of the system algebraically. Furthermore we show that the model is multiseparable and allows separation of variables in the hyperspherical and parabolic coordinates. We also show the separability of its 8D dual system (i.e. the 8D singular harmonic oscillator) in the Euler and cylindrical coordinates.