Russian Physics Journal

, Volume 58, Issue 12, pp 1816–1825 | Cite as

Integrability of the Wong Equations in the Class of Linear Integrals of Motion

ELEMENTARY PARTICLE PHYSICS AND FIELD THEORY
First Online:
Received:
  • 35 Downloads

The Wong equations, which describe the motion of a classical charged particle with isospin in an external gauge field, are considered. The structure of the Lie algebra of the linear integrals of motion of these equations is investigated. An algebraic condition for integrability of the Wong equations is formulated. Some examples are considered.

Keywords

Wong equations integral of motion integrability 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. K. Wong, Il Nuovo Cimento, A65, 689–694 (1970).ADSCrossRefGoogle Scholar
  2. 2.
    R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York (1965).MATHGoogle Scholar
  3. 3.
    D. V. Gal’tsov, Yu. V. Grats, and V. Ts. Zhukovskii, Textbook in Classical Fields, Izd. MGU, Moscow (1991).Google Scholar
  4. 4.
    V. G. Bagrov and A. S. Vishvstev, Motion of a Non-Abelian Particle in Color Fields, Preprint No. 14, Tomsk Affiliate of the Siberian Branch of the Academy of Sciences of the USSR (1987).Google Scholar
  5. 5.
    A. W. Wipf, J. Phys., A18, No. 12, 2379 (1985).ADSMathSciNetGoogle Scholar
  6. 6.
    L. Gy. Feher, J. Phys., A19, No. 7, 1259–1270 (1986).ADSMathSciNetGoogle Scholar
  7. 7.
    S. Sternberg, Proc. Nat. Acad. Sci., 74, No. 12, 5253–5254 (1977).ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    A. Weinstein, Lett. Math. Phys., 2, No. 5, 417–420 (1978).ADSCrossRefGoogle Scholar
  9. 9.
    J. W. Van Holten, Phys. Rev., D75, No. 2, 025027 (2007).ADSGoogle Scholar
  10. 10.
    A. S. Mishchenko and A. T. Fomenko, Funkts. Anal. Prilozh., 12, No. 2, 46–56 (1978).Google Scholar
  11. 11.
    I. V. Gaishun, Completely Solvable Multidimensional Differential Equations [in Russian], Editorial URSS, Moscow (2004).Google Scholar
  12. 12.
    D. Alekseevsky, P. W. Michor, and W. Ruppert, arXiv preprint math/0005042. – 2000.Google Scholar
  13. 13.
    A. A. Magazev, Russ. Phys. J., 57, No. 3, 312–320 (2014).CrossRefGoogle Scholar
  14. 14.
    T. T. Wu and C. N. Yang, Properties of Matter under Unusual Conditions, H. Mark and S. Fernbach, eds., Interscience Publ., New York (1969).Google Scholar
  15. 15.
    J. A. Smoller et al., Commun. Math. Phys., 143, No. 1, 115–147 (1991).ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Omsk State Technical UniversityOmskRussia

Personalised recommendations