Relative variables of the exact fermion-antifermion bound state wave-function in the Schwinger Model

TL;DR

This paper analyzes the exact fermion-antifermion bound state wave-function in the Schwinger Model, focusing on its dependence on relative variables and revealing key properties like threshold structures.

Contribution

It provides a detailed analysis of the Bethe-Salpeter amplitude's dependence on relative variables in all instanton sectors in the Schwinger Model.

Findings

Explicit threshold structure demonstrated

Dependence on relative time and position analyzed

Dependence on relative energy and momentum analyzed

Abstract

The exact Bethe-Salpeter amplitude for the fermion-antifermion bound state in the Schwinger Model is investigated. The dependence on the relative time and position in the center-of-mass frame in all contributing instanton sectors is analyzed. The same is accomplished for the relative energy and momentum variables. Several interesting properties of the amplitude are revealed. The explicit threshold structure is demonstrated.