Russian Physics Journal

, Volume 62, Issue 1, pp 12–22 | Cite as

Stable Interactions Between the Extended Chern-Simons Theory and a Charged Scalar Field with Higher Derivatives: Hamiltonian Formalism

  • V. A. AbakumovaEmail author
  • D. S. Kaparulin
  • S. L. Lyakhovich

The constrained Hamiltonian formalism for the extended higher derivative Chern–Simons theory of an arbitrary finite order is considered. It is shown that the n-th order theory admits an (n–1)-parametric series of conserved tensors. It is clarified that this theory admits a series of canonically non-equivalent Hamiltonian formulations, where a zero-zero component of any conserved tensor can be chosen as a Hamiltonian. The canonical Ostrogradski Hamiltonian is included into this series. An example of interactions with a charged scalar field is also given, which preserve the selected representative of the series of Hamiltonian formulations.


higher-derivative theories Hamiltonian formalism extended Chern–Simons theory 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. V. Ostrogradski, Mem. Acad. St. Petersburg, 6, 385–517 (1850).Google Scholar
  2. 2.
    D. M. Gitman, S. L. Lyakhovoich, and I. V. Tyutin, Sov. Phys. J., 26, No. 8, 730– 734 (1983).CrossRefGoogle Scholar
  3. 3.
    J. Kluson, M. Oksanen, and A. Tureanu, Phys. Rev. D, 89, 064043 (2014).CrossRefGoogle Scholar
  4. 4.
    Y. Ohkuwa, Y. Ezawa, and S. Templeton, Eur. Phys. J. Plus., 77, 130 (2015).Google Scholar
  5. 5.
    E. T. Tomboulis, Mod. Phys. Lett. A, 30, 1540005 (2015).MathSciNetCrossRefGoogle Scholar
  6. 6.
    M. Pavsic, Int. J. Geom. Meth. Mod. Phys., 13, 1630015 (2016).CrossRefGoogle Scholar
  7. 7.
    A. V. Smilga, Int. J. Mod. Phys. A, 32, 1730025 (2017).MathSciNetCrossRefGoogle Scholar
  8. 8.
    K. Bolonek and P. Kosinski, Acta Phys. Polon. B, 36, 2115–2131 (2005).Google Scholar
  9. 9.
    E. V. Damaskinsky and M. A. Sokolov, J. Phys. A, 39, 10499 (2006).MathSciNetCrossRefGoogle Scholar
  10. 10.
    D. S. Kaparulin, S. L. Lyakhovich, and A. A. Sharapov, Eur. Phys. J. С., 74, 3072 (2014).CrossRefGoogle Scholar
  11. 11.
    V. A. Abakumova, D. S. Kaparulin, and S. L. Lyakhovich, Eur. Phys. J. С., 78, 115 (2018).CrossRefGoogle Scholar
  12. 12.
    V. A. Abakumova, D. S. Kaparulin, and S. L. Lyakhovich, Russ. Phys. J., 60, No. 12, 2095–2104 (2018).CrossRefGoogle Scholar
  13. 13.
    S. Deser and R. Jackiw, Phys. Lett. B, 451, 73–76 (1999).MathSciNetCrossRefGoogle Scholar
  14. 14.
    D. S. Kaparulin, I.Yu. Karataeva, and S. L. Lyakhovich, Eur. Phys. J. C., 75, 552 (2015).CrossRefGoogle Scholar
  15. 15.
    V. A. Abakumova, D. S. Kaparulin, and S. L. Lyakhovich, Phys. Rev. D. 99, 045020 (2019).CrossRefGoogle Scholar
  16. 16.
    T. Ehrhardt and K. Rost, Linear Algebra and its Applications, 439, 621–639 (2013).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • V. A. Abakumova
    • 1
    Email author
  • D. S. Kaparulin
    • 1
  • S. L. Lyakhovich
    • 1
  1. 1.National Research Tomsk State UniversityTomskRussia

Personalised recommendations