This article is designed to focus attention on the Markov-Yukawa
Transversality Principle (MYTP) as a novel paradigm for an exact 3D-4D
interlinkage between the corresponding BSE amplitudes, with a closely parallel
treatment of qqˉ and qqq systems, stemming from a common 4-fermion
Lagrangian mediated by gluon (vector)-like exchange. This unique feature of
MYTP owes its origin to a Lorentz- covariant 3D support to the BS kernel, which
acts as a sort of `gauge principle' and distinguishes it from most other 3D
approaches to strong interaction dynamics. Some of the principal approaches in
the latter category are briefly reviewed so as to set the (less familiar) MYTP
in their context. Two specific types of MYTP which provide 3D support to the
BSE kernel, are considered: a) Covariant Instantaneity Ansatz (CIA); b)
Covariant LF/NP ansatz (Cov.LF). Both lead to formaly identical 3D BSE
reductions but produce sharply different 4D structures: Under CIA, the 4D loop
integrals suffer from Lorentz mismatch of the vertex functions, leading to
ill-defined time-like momentum integrals, but Cov LF is free from this disease.
This is illustrated by the pion form factor under Cov LF. The reconstruction of
the 4D qqq wave function is achieved by Green's function techniques. PACS:
11.10 st ; 12.38 Lg ; 13.40.Fn. Keywords: Tamm-Dancoff, Bethe-Salpeter,
Quasi-potentials, Light-front (LF), Markov-Yukawa, 3D-4D Interlinkage, CIA,
Cov-LF, Spectroscopy.Comment: Latex file 38 pp; to appear in the Proceedings of the XXIII Intl.
Workshop on Fundamental Problems in QFT, Protvino, June 200
