Lagrangian and Hamiltonian formalisms for relativistic dynamics of a charged particle with dipole moment

  • A. Peletminskii
  • S. Peletminskii
Theoretical Physics


The Lagrangian and Hamiltonian formulations for the relativistic classical dynamics of a charged particle with dipole moment in the presence of an electromagnetic field are given. The differential conservation laws for the energy-momentum and angular momentum tensors of a field and particle are discussed. The Poisson brackets for basic dynamic variables, which form a closed algebra, are found. These Poisson brackets enable us to perform the canonical quantization of the Hamiltonian equations that leads to the Dirac wave equation in the case of spin 1/2. It is also shown that the classical limit of the squared Dirac equation results in equations of motion for a charged particle with dipole moment obtained from the Lagrangian formulation. The inclusion of gravitational field and non-Abelian gauge fields into the proposed formalism is discussed.


Dipole Moment Charged Particle Dirac Equation Poisson Bracket Gauge Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ya.V. Frenkel, Z. Phys. 37, 243 (1926)CrossRefGoogle Scholar
  2. 2.
    L.H. Thomas, Phil. Mag. 3, 1 (1927)Google Scholar
  3. 3.
    V. Bargmann, L. Michel, V.L. Telegdi, Phys. Rev. Lett. 2, 435 (1959)CrossRefGoogle Scholar
  4. 4.
    S.R. de Groot, L.G. Suttorp, Foundations of electrodynamics (North-Holland Publishing Company, Amsterdam 1972); and references cited thereinGoogle Scholar
  5. 5.
    G. Cognola, L. Vanzo, S. Zerbini, R. Soldati, Phys. Lett. B 104, 67 (1981)CrossRefGoogle Scholar
  6. 6.
    A.J. Hanson, T. Regge, Ann. Phys. 87, 498 (1974)CrossRefGoogle Scholar
  7. 7.
    P. Grassberger, J. Phys. A: Math. Gen. II, 1221 (1978)Google Scholar
  8. 8.
    R. Amorim, J. Math. Phys. 25, 874 (1984)CrossRefGoogle Scholar
  9. 9.
    C. Itzykson, A. Voros, Phys. Rev. D 5, 2939 (1972)CrossRefGoogle Scholar
  10. 10.
    D.V. Volkov, A.A. Zheltukhin, Izv. Akademii Nauk USSR, Ser. Fiz. 44, 1487 (1980) [in Russian]Google Scholar
  11. 11.
    A.A. Isayev, M.Yu. Kovalevskii, S.V. Peletminskii, Fiz. Elem. Chastits. At. Yadra, 27, 431 (1996) [Phys. Part. Nuclei 27, 203 (1996)]Google Scholar
  12. 12.
    S.R. de Groot, W.A. van Leeuwen, Ch.G. van Weert, Relativistic kinetic theory. Principles and applications (North-Holland Publishing, Amsterdam 1980)Google Scholar
  13. 13.
    T.W. Kibble, J. Math. Phys. 2, 212 (1961)CrossRefGoogle Scholar
  14. 14.
    J.W. van Holten, Nucl. Phys. B 356, 3 (1991)CrossRefGoogle Scholar
  15. 15.
    J. Schwinger, Quantum kinematics and dynamics (W.A. Benjamin Inc., New York 1970)Google Scholar
  16. 16.
    D.V. Volkov, S.V. Peletminskii, Zh. Eksp. Teor. Fiz. 37, 170 (1959) [Sov. Phys. JETP 37, 121 (1960)]Google Scholar
  17. 17.
    R.P. Feynman, M. Gell-Mann, Phys. Rev. 109, 193 (1958)CrossRefGoogle Scholar
  18. 18.
    W.G. Dixon, Nuovo Cimento 38, 1616 (1965)Google Scholar
  19. 19.
    G. Cognola, R. Soldati, L. Vanzo, S. Zerbini, Nuovo Cimento B 76, 109 (1983)Google Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2005

Authors and Affiliations

  • A. Peletminskii
    • 1
    • 2
  • S. Peletminskii
    • 1
  1. 1.National Science Centre Kharkov Institute of Physics and TechnologyKharkovUkraine
  2. 2.The Abdus Salam International Centre for Theoretical PhysicsTriesteItaly

Personalised recommendations