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

Abstract

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

Lorentz contraction of the equal-time Bethe–Salpeter amplitude in two-dimensional massless quantum electrodynamics

“…For this goal we need a real scalar function. Similarly to what we did in our previous work [45,46], we define two gauge invariant quantities:…”