Minkowski Space Dynamics and Light-Front Projection

TL;DR

This paper investigates the relationship between Minkowski-space Bethe-Salpeter equations and light-front projection, focusing on bound-state dynamics with dressed particles and applications to hadron structure.

Contribution

It introduces a formal framework connecting four-dimensional Minkowski-space dynamics with three-dimensional light-front approaches, including dressed particles and three-body systems.

Findings

Coupling of valence and higher Fock components in dressed particle systems

Derivation of light-front Faddeev-Bethe-Salpeter equations for three-body systems

Application to hadron structure studies

Abstract

We explore the connection between the four-dimensional Minkowski-space Bethe-Salpeter equation and its light-front projection, emphasizing the implications for bound-state dynamics. Our approach incorporates dressed particles, such as quarks, via the integral representation of the corresponding propagator. We analyze the light-front dynamics of the valence component of the physical state using a hierarchical set of Green's functions, which reveals its coupling to higher Fock components when dressed particles are considered. We also present the light-front Faddeev-Bethe-Salpeter equations for three-body systems with dressed constituents. Furthermore, we discuss formal developments that are central to connecting the three-dimensional light-front dynamics onto the null-plane and the four-dimensional Minkowski-space framework, based on the Nakanishi integral representation. Selected applications to hadron structure are also reviewed.