Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-04-10
Nucl.Phys. A696 (2001) 581-604
Physics
High Energy Physics
High Energy Physics - Theory
22 pages, 3 figures in one single ps file. In the first revision, the self-energy corrections to the propagator have been take
Scientific paper
10.1016/S0375-9474(01)01134-4
We perform a 3D reduction of the two-fermion Bethe-Salpeter equation, by series expansion around a positive-energy instantaneous approximation of the Bethe-Salpeter kernel, followed by another series expansion at the 3D level in order to get a manifestly hermitian 3D potential. It turns out that this potential does not depend on the choice of the starting approximation of the kernel anymore, and can be written in a very compact form. This result can also be obtained directly by starting with an approximation of the free propagator, based on integrals in the relative energies instead of the more usual delta-constraint. Furthermore, the method can be generalized to a system of N particles, consisting in any combination of bosons and fermions. As an example, we write the 3D equation for systems of two or three fermions exchanging photons, in Feynman or Coulomb's gauge.
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