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arXiv · 1212.1663

Isospin particle systems on quaternionic projective spaces

Stefano Bellucci·Sergey Krivonos·Armen Nersessian·Vahagn Yeghikyan
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Abstract

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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Stefano Bellucci, Sergey Krivonos, Armen Nersessian, Vahagn Yeghikyan. 2012-12-12. Isospin particle systems on quaternionic projective spaces. https://doi.org/10.1103/physrevd.87.045005

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