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

TL;DR

This review discusses projecting the Bethe-Salpeter equation onto the Light-Front surface, highlighting the relation to effective valence dynamics, Fock expansion construction, and generalization to three-particle systems.

Contribution

It provides an overview of the Light-Front projection method for the Bethe-Salpeter equation and details on constructing consistent operators and extending to three particles.

Findings

Relation between projection method and valence wave function dynamics

Construction of Light-Front effective interaction and current operators

Outline of three-particle generalization

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.