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Isospin particle systems on quaternionic projective spaces

Stefano Bellucci1, Sergey Krivonos2, Armen Nersessian3, and Vahagn Yeghikyan1,3

  • 1INFN-Laboratori Nazionali di Frascati,Via E. Fermi 40, 00044 Frascati, Rome, Italy
  • 2Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia
  • 3Yerevan State University, 1 Alex Manoogian Street, Yerevan 0025, Armenia

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Phys. Rev. D 87, 045005 – Published 7 February, 2013

DOI: https://doi.org/10.1103/PhysRevD.87.045005

Abstract

We construct the isospin particle system on n-dimensional quaternionic projective spaces in the presence of the Belavin-Polyakov-Schwarz-Tyupkin 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 oscillatorlike system is superintegrable. We show that, besides the analogs of quadratic constants of motion of the spherical (Higgs) and CPn oscillators, it possesses the third-order constants of motion, which are functionally independent from the quadratic ones.

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Phys. Rev. D 87, 045005– Published 7 February, 2013
  • Received 12 December 2012

© 2013 American Physical Society

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