https://doi.org/10.1140/epja/i2009-10823-5
Regular Article - Theoretical Physics
A generalization of the Fermi-Breit equation to non-Coulombic spatial interactions
Departamento de Física, Universidad Nacional de Colombia, Bogotá D. C., Colombia
* e-mail: maurizio.desanctis@roma1.infn.it
Received:
12
March
2008
Revised:
1
June
2009
Accepted:
6
June
2009
Published online:
16
July
2009
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 –
© SIF, Springer-Verlag Berlin Heidelberg, 2009
