Light-Front QCD: Role of Longitudinal Boundary Integrals

TL;DR

This paper investigates the role of boundary integrals in light-front QCD, showing they cancel infrared divergences and influence the asymptotic behavior of gauge fields, revealing topological and non-local effects.

Contribution

It demonstrates that proper treatment of boundary integrals in light-front QCD cancels infrared divergences and determines gauge field behavior at infinity, highlighting topological and non-local phenomena.

Findings

Boundary integrals cancel light-front infrared divergences.

Asymptotic gauge fields are influenced by boundary conditions.

Topological winding numbers emerge from boundary integrals.

Abstract

In the canonical light-front QCD, the elimination of unphysical gauge degrees of freedom leads to a set of boundary integrals which are associated with the light-front infrared singularity. We find that a consistent treatment of the boundary integrals leads to the cancellation of the light-front linear infrared divergences. For physical states, the requirement of finite energy density in the light-front gauge $(A_a^+=0)$ results in equations which determine the asymptotic behavior of the transverse (physical) gauge degrees of freedom at longitudinal infinity. These asymptotic fields are generated by the boundary integrals and they are responsible for the topological winding number. They also involve non-local behavior in the transverse direction that leads to non-local forces.