3D reduction of the N-body Bethe-Salpeter equation
Abstract
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.
Cite
@article{arxiv.hep-th/0004060,
title = {3D reduction of the N-body Bethe-Salpeter equation},
author = {J. Bijtebier},
journal= {arXiv preprint arXiv:hep-th/0004060},
year = {2009}
}
Comments
22 pages, 3 figures in one single ps file. In the first revision, the self-energy corrections to the propagator have been taken into account. The three figures were gathered in a single ps file instead of three eps. In this second revision (after submission to Nuclear Physics A and refereeing) some explanations have been added, plus a new subsection about the scattering of a particle by a bound state