Interlinked 3D and 4D 3-quark wave functions in a Bethe-Salpeter model

Abstract

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 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 qq̅ interaction. The generalization from spinless to fermion quarks is straightforward.