Interlinked 3D and 4D 3-Quark Wave Functions in a Bethe-Salpeter Model

Details Interlinked 3D and 4D 3-Quark Wave Functions in a Bethe-Salpeter Model Interlinked 3D and 4D 3-Quark Wave Functions in a Bethe-Salpeter Model

1996-11-18

arxiv.org/abs/hep-th/9611129v1

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, Latex. e.mail: csec@doe.ernet.in

Scientific paper

Using the method of Green's functions within the framework of a Bethe-Salpeter formalism characterized by a pairwise $qq$ interaction with a 3D support to its kernel (expressed in a Lorentz-covariant manner), the 4D BS wave function for a system of three identical relativistic spinless quarks is reconstructed from the corresponding 3D form which satisfies a {\it fully connected} 3D BSE. This result is a 3-body generalization of a similar interconnection between the 3D and 4D 2-body wave functions that had been found earlier under identical conditions of a 3D support to the corresponding BS kernel, using the ansatz of Covariant Instaneity for the pairwise $q\bar q$ interaction. The generalization from spinless to fermion quarks is straightforward.

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