Projecting the Bethe-Salpeter Equation onto the Light-Front and back: A Short Review

Abstract

The technique of projecting the four-dimensional two-body Bethe-Salpeter equation onto the three-dimensional Light-Front hypersurface, combined with the quasi-potential approach, is briefly illustrated, by placing a particular emphasis on the relation between the projection method and the effective dynamics of the valence component of the Light-Front wave function. Some details on how to construct the Fock expansion of both i) the Light-Front effective interaction and ii) the electromagnetic current operator, satisfying the proper Ward-Takahashi identity, will be presented, addressing the relevance of the Fock content in the operators living onto the Light-Front hypersurface. Finally, the generalization of the formalism to the three-particle case will be outlined.

16 pages, macros included. Mini-review to be printed in a regular issue of Few-Body Systems devoted to the Workshop on "Relativistic Description of Two- and Three-body Systems in Nuclear Physics" ECT* Trento, 19 - 23 October 2009

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Cited by in corpus (19)

• Efimov Physics: a review
• Two-body scattering states in Minkowski space and the Nakanishi integral representation onto the null plane
• Towards three-body unitarity in $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$
• Bethe-Salpeter bound-state structure in Minkowski space
• Light-Front projection of spin-1 electromagnetic current and zero-modes
• Observing the Minkowskian dynamics of the pion on the null-plane
• Fermionic bound states in Minkowski-space: Light-cone singularities and structure
• Going to the light front with contour deformations
• Final state interaction in $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ with $K\pi$ I=1/2 and 3/2 channels
• Exploring the flavor content of light and heavy-light pseudoscalars
• Excited states of the Wick-Cutkosky model with the Nakanishi representation in the Light-Front framework
• Two-fermion Bethe-Salpeter Equation in Minkowski Space: the Nakanishi Way
• Proton image and momentum distributions from light-front dynamics
• Solutions of the Bethe-Salpeter Equation in Minkowski space: a comparative study
• Proton quark distributions from a light-front Faddeev-Bethe-Salpeter approach
• Pion inspired by QCD: Nakanishi and Light-Front Integral Representations
• Heavy meson decay in three-mesons and FSI
• Covariant analysis of electromagnetic current on the light cone: exposition with scalar Yukawa theory
• Relativistic Borromean States