Minkowski Space Dynamics and Light-Front Projection

TL;DR

The paper addresses the challenge of describe relativistic bound states by bridging the four-dimensional Minkowski-space Bethe–Salpeter equation (BSE) with its light-front (LF) projection, employing the Nakanishi integral representation (NIR) and dressed propagators to access timelike observables. The authors develop a quasi-potential framework that maps the Minkowski-space dynamics to a three-dimensional LF problem, derive hierarchical LF Green’s function relations that reveal coupling to higher Fock components, and extend the LF projection to three-body systems via Faddeev–Bethe–Salpeter equations for dressed constituents. By solving the BSE in Minkowski space with NIR, they obtain a direct route to LF valence wave functions and to hadron observables such as form factors, generalized parton distributions, and structure functions, with applications to pion structure and beyond. The framework offers a covariant, nonperturbative bridge between fundamental QCD dynamics and three-dimensional hadron imaging, with practical implications for interpreting future high-precision data from facilities like the Electron-Ion Collider (EIC).

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.