Physics of Particles and Nuclei Letters

, Volume 11, Issue 7, pp 1003–1005 | Cite as

On integrable isospin particle system on high dimensional quaternionic systems



We explicitly construct the projection map of a fibration of odd-dimensional complex projective space over quaternionic projective one. Performing a Hamiltonian reduction by U(1) subset of the isometries of both total space and bundle we construct an integrable system of free particle on ℍℙn with the presence of Yang’s monopole.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. Duval and P. Horvathy, “Particles with internal structure: the geometry of classical motions and conservation laws,” Annals Phys. 142, 10 (1982).ADSCrossRefMathSciNetGoogle Scholar
  2. 2.
    S.-C. Zhang and J.-P. Hu, “A four-dimensional generalization of the quantum hall effect,” Science 294, 823 (2001) [cond-mat/0110572].ADSCrossRefGoogle Scholar
  3. 3.
    B. A. Bernevig, C. H. Chern, J. P. Hu, N. Toumbas, and S. C. Zhang, “Effective field theory description of the higher dimensional quantum hall liquid,” Annals Phys. 300, 185 (2002); M. Fabinger, “Higher-dimensional quantum hall effect in string theory,” JHEP 0205, 037 (2002).ADSCrossRefMathSciNetMATHGoogle Scholar
  4. 4.
    D. Karabali and V. P. Nair, “Quantum Hall effect in higher dimensions, matrix models and fuzzy geometry,” J. Phys. A 39, 12735 (2006) [hep-th/0606161].ADSCrossRefMathSciNetMATHGoogle Scholar
  5. 5.
    S. Bellucci, S. Krivonos, A. Nersessian, and V. Yeghikyan, “Isospin particle systems on quaternionic projective spaces,” Phys. Rev. D 87, 045005 (2013).ADSCrossRefGoogle Scholar
  6. 6.
    S. Bellucci, P.-Y. Casteill, and A. Nersessian, “Fourdimensional hall mechanics as a particle on CP**3,” Phys. Lett. B 574, 121 (2003) [hep-th/0306277].ADSCrossRefMathSciNetMATHGoogle Scholar
  7. 7.
    S. Bellucci and A. Nersessian “(Super)oscillator on CP**N and constant magnetic field,” Phys. Rev. D 67, 065013 (2003); Phys. Rev. D 71, 089901(E) (2005), arXiv:hep-th/0211070.ADSCrossRefGoogle Scholar
  8. 8.
    P. W. Higgs, “Dynamical symmetries in a spherical geometry,” J. Phys. A: Math. Gen. 12, 309 (1979); H. I. Leemon, “Dynamical symmetries in a spherical geometry. 2,” J. Phys. A 12, 489 (1979).ADSCrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Yerevan State UniversityYerevanArmenia

Personalised recommendations