3D-4D interlinkage of B-S amplitudes: unified view of QQ̅ and QQQ dynamics

Mitra, A. N. (1999) 3D-4D interlinkage of B-S amplitudes: unified view of QQ̅ and QQQ dynamics Arxiv-eprints . pp. 1-37.

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Official URL: http://arxiv.org/pdf/hep-ph/9912239v1.pdf


This article has a 3-fold objective: i) to provide a panoramic view of several types of 3D vs 4D approaches in Field Theory (Tamm-Dancoff, Bethe Salpeter Equation (BSE), Quasi-potentials, Light-Front Dynamics, etc) for strong interaction dunamics; ii) to focus on the role of the Markov-Yukawa Transversality Principle (MYTP) as a novel paradigm for an exact 3D-4D interlinkage between the corresponding BSE amplitudes; iii) Stress on a closely parallel treatment of qq̅ and qqq BSE's stemming from a common 4-fermion Lagrangian mediated by gluon (vector)-like exchange. The two-way interlinkage offered by MYTP between the 3D and 4D BSE forms via a Lorentz-covariant 3D support to the BS kernel, gives it a unique status which distinguishes it from most other 3D approaches to strong interaction dynamics, which give at most a one-way connection. 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 (thus ensuring common spectral predictions), but their 4D manifestations differ sharply: 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. Some practical uses of MYTP as a basis for evaluating various types of 4D loop integrals are outlined.

Item Type:Article
Source:Copyright of this article belongs to Arxiv Publications.
Keywords:Tamm-Dancoff; Bethe-Salpeter; Quasi-potentials; Light-front (LF); Markov-Yukawa; 3D-4D Interlinkage; CIA; Cov-LF; Spectroscopy
ID Code:90192
Deposited On:07 May 2012 13:13
Last Modified:19 May 2016 04:28

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