3D-4D Interlinkage Of qqq Wave Functions Under 3D Support For Pairwise Bethe-Salpeter Kernels

Details 3D-4D Interlinkage Of qqq Wave Functions Under 3D Support For Pairwise Bethe-Salpeter Kernels 3D-4D Interlinkage Of qqq Wave Functions Under 3D Support For Pairwise Bethe-Salpeter Kernels

1998-03-07

arxiv.org/abs/hep-th/9803062v1

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, Latex, submitted via the account of K.-C. Yang

Scientific paper

10.1142/S0217751X99002256

Using the method of Green's functions within a Bethe-Salpeter framework characterized by a pairwise qq interaction with a Lorentz-covariant 3D support to its kernel, the 4D BS wave function for a system of 3 identical relativistic spinless quarks is reconstructed from the corresponding 3D form which satisfies a fully connected 3D BSE. This result is a 3-body generalization of a similar 2-body result found earlier under identical conditions of a 3D support to the corresponding qq-bar BS kernel under Covariant Instaneity (CIA for short). (The generalization from spinless to fermion quarks is straightforward). To set the CIA with 3D BS kernel support ansatz in the context of contemporary approaches to the qqq baryon problem, a model scalar 4D qqq BSE with pairwise contact interactions to simulate the NJL-Faddeev equations is worked out fully, and a comparison of both vertex functions shows that the CIA vertex reduces exactly to the NJL form in the limit of zero spatial range. This consistency check on the CIA vertex function is part of a fuller accounting for its mathematical structure whose physical motivation is traceable to the role of `spectroscopy' as an integral part of the dynamics.

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