Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-07-15
J.Phys.G26:871-886,2000
Physics
High Energy Physics
High Energy Physics - Theory
21 pages, 1 figure This article has been deeply modified after refereeing. The presentation has been improved and examples hav
Scientific paper
10.1088/0954-3899/26/6/310
We perform a 3D reduction of the two-fermion Bethe-Salpeter equation based on Sazdjian's explicitly covariant propagator, combined with a covariant substitute of the projector on the positive-energy free states. We use this combination in the two fermions in an external potential and in the three-fermion problems. The covariance of the two-fermion propagators insures the covariance of the two-body equations obtained by switching off the external potential, or by switching off all interactions between any pair of two fermions and the third one, even if the series giving the 3D potential is limited to the Born term or more generally truncated. The covariant substitute of the positive energy projector preserves the equations against continuum dissolution without breaking the covariance.
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