Relative energy dependence of the Bethe-Salpeter amplitude in two-dimensional massless QED

TL;DR

This paper studies the Bethe-Salpeter bound state amplitude in 2D massless QED, revealing energy-dependent singularities linked to quark thresholds for Schwinger boson creation, confirmed through analysis and numerical plots.

Contribution

It provides a detailed analysis of the energy dependence of the Bethe-Salpeter amplitude in 2D massless QED, highlighting singularities at specific energy thresholds.

Findings

Singularities in the amplitude occur at quark energy thresholds.

Analytical and numerical methods confirm the presence of these singularities.

Results enhance understanding of bound states in lower-dimensional QED.

Abstract

The exact $q\bar{q}$ Bethe-Salpeter bound state amplitude is investigated in the space of relative energy $E$ for fixed value of relative position. By means of approximate analysis it is shown to possess singularities in $E$ whenever one of the quarks reaches the energy threshold for the creation of certain number of Schwinger bosons. These results are afterwards confirmed by numerical plots.