Singularity-softening prescription for the Bethe-Salpeter equation

TL;DR

This paper introduces a singularity-softening prescription for the Bethe-Salpeter equation in light-front dynamics, effectively canceling kernel singularities at zero plus momentum of the gauge, and enabling perturbative expansion in the coupling constant.

Contribution

It proposes a novel singularity-softening method for the Bethe-Salpeter equation in light-front gauge, improving the treatment of kernel singularities and facilitating perturbative analysis.

Findings

Exact cancellation of kernel singularities at zero plus momentum

Perturbative expansion in powers of the coupling constant g

Enhanced stability of the integral equation solution

Abstract

The reduction of the two fermion Bethe-Salpeter equation in the framework of light-front dynamics is studied for one gauge A+=0. The arising effective interaction can be perturbatively expanded in powers of the coupling constant g, allowing a defined number of gauge boson exchanges. The singularity of the kernel of the integral equation at vanishs plus momentum of the gauge is canceled exactly in on approuch. We studied the problem using a singularity-softening prescription for the light-front gauge.