Towards a 3D reduction of the N-body Bethe-Salpeter equation

Details Towards a 3D reduction of the N-body Bethe-Salpeter equation Towards a 3D reduction of the N-body Bethe-Salpeter equation

2000-10-17

arxiv.org/abs/hep-th/0010132v1

Physics

High Energy Physics

High Energy Physics - Theory

4 pages. Poster presented at the XVIIth conference on few-body problems in physics, Evora 2000

Scientific paper

Starting with the homogeneous Bethe-Salpeter equation for two fermions, we perform a 3D reduction using a series expansion around an unspecified positive-energy instantaneous approximation of the kernel. A second series expansion is made, at the 3D level, in order to get an "hermitian" potential. The combination of both series gives a very simple result, which does not depend of the initial approximation of the kernel anymore, and could be obtained directly by starting with an approximation of the free propagator. The generalisation of this result to a system of f (=0,...N) fermions and N-f bosons is easy.

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