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

  • A. Peletminskii
  • S. Peletminskii
Theoretical Physics

Abstract.

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.

Keywords

Dipole Moment Charged Particle Dirac Equation Poisson Bracket Gauge Field 

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References

  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

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