The European Physical Journal A

, Volume 41, Issue 2, pp 169–178 | Cite as

A generalization of the Fermi-Breit equation to non-Coulombic spatial interactions

  • M. De SanctisEmail author
Regular Article - Theoretical Physics


Starting from the relativistic invariance properties at classical level, we generalize the Darwin equation to the case of non-Coulombic spatial interactions. The relativistic correction terms for vector interactions are derived from a given nonrelativistic potential. We show that, for a Coulombic potential, the results coincide with those obtained in the Coulomb gauge. The results are adapted to the quantum theory obtaining a generalization of the Fermi-Breit equation. An Hermitian interaction operator is constructed. A critical comparison with other possible treatments of the retardation terms is performed also discussing the usual choice of the Coulomb gauge. Special attention is devoted to the construction of a model for quark interaction.


03.50.De Classical electromagnetism, Maxwell equations 11.10.Ef Lagrangian and Hamiltonian approach 11.30.Cp Lorentz and Poincaré invariance 12.39.Ki Relativistic quark model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. Sucher, What is force between electrons? preprint, arXiv:hep-ph/9706219v1.Google Scholar
  2. 2.
    L.D. Landau, E.M. Lifshits, The Classical Theory of Fields, fourth edition (Butterworth-Heinemann, Amsterdam, 1995) p. 179.Google Scholar
  3. 3.
    J.D. Jackson, Classical Electrodynamics, second edition (John Wiley and Sons, New York, 1975) p. 593.Google Scholar
  4. 4.
    H.C. Pauli, Eur. Phys. J. A 19, s01, 15 (2004).Google Scholar
  5. 5.
    M. De Sanctis, P. Quintero, Eur. Phys. J. A 39, 145 (2009).Google Scholar
  6. 6.
    M. De Sanctis, P. Quintero, in preparation.Google Scholar
  7. 7.
    E.G. Bessonov, On the Darwin Lagrangian, preprint, arXiv:physics/9902065v3.Google Scholar
  8. 8.
    E. Eichten, Phys. Rev. Lett. 34, 369 (1975)Google Scholar
  9. 9.
    I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New York, 1980) eq. (3.944.11).Google Scholar
  10. 10.
    V.B. Berestetskii, L.P. Pitaevskii, E.M. Lifshitz, Quantum Electrodynamics, Vol. 4, second edition (Elsevier, Butterworth Heinemann, Oxford, 1982) pp. 126, 336, 626.Google Scholar
  11. 11.
    D. Ebert, R.N. Faustov, V.O. Galkin, Eur. Phys. J. C 7, 539 (1999).Google Scholar
  12. 12.
    H.C. Pauli, Fine and Hyperfine interaction on the light cone, preprint, arXiv:hep-ph/0312298v1.Google Scholar
  13. 13.
    J. Eiglsperger, Quarkonium Spectroscopy: Beyond One-Gluon Exchange, Diploma Thesis, Technisce Universität München 2007, preprint, arXiv:0707.1269v1 and references therein.Google Scholar
  14. 14.
    D. Ebert, R.N. Faustov, V.O. Galkin, Phys. Rev. D 62, 034014 (2000).Google Scholar
  15. 15.
    Cong-Feng Qiao, Han-Wen Huang, Kuang-Ta Chao, Phys. Rev. D 60, 094004 (1999).Google Scholar
  16. 16.
    M. De Sanctis, D. Prosperi, Nuovo Cimento A 107, 611 (1994).Google Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Departamento de FísicaUniversidad Nacional de ColombiaBogotá D. C.Colombia

Personalised recommendations