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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

Abstract

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.

PACS

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 

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Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

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

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