四元数射影空间上的同位旋粒子系统
Isospin particle systems on quaternionic projective spaces
摘要：
通过对$(2n+1)$维复射影空间上自由粒子的约化，在BPST瞬子存在的情况下，构造了$n$维四元数射影空间上的同位旋粒子系统.然后，我们添加到这个系统的“四元数振子势”，并表明，这个类振子系统是超可积的。我们表明，除了类似的二次运动常数的球形（希格斯）和$\mathbb{C}P^n $振荡器，它具有三阶运动常数，这是功能上独立于二次。
英文摘要：
We construct the isospin particle system on $n$-dimensional quaternionic projective spaces in the presence of BPST-instanton by the reduction from the free particle on $(2n+1)$-dimensional complex projective space. Then we add to this system a "quaternionic oscillator potential" and show, that this oscillator-like system is superintegrable. We show, that besides the analogs of quadratic constants of motion of the spherical (Higgs) and $\mathbb{C}P^n $- oscillators, it possesses the third-order constants of motion, which are functionally independent from the quadratic ones.
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