Restoration of the residue factorizability in the bound-state pole by instanton-antiinstanton configurations

TL;DR

This paper demonstrates that instanton-antiinstanton configurations restore the residue factorizability in the bound-state pole of the Schwinger Model by canceling unwanted contributions in the four-point Green function.

Contribution

It shows that instanton-antiinstanton effects are crucial for restoring residue factorizability in the Schwinger Model's bound-state pole, highlighting their role in nonperturbative phenomena.

Findings

Instanton-antiinstanton configurations cancel unwanted terms.

Residue factorizability is restored in the bound-state pole.

The four-point Green function reflects these effects.

Abstract

The instanton-antiinstnton contributions to the $q\overline{q}$ bound state pole in the four-point Green function in the Schwinger Model are calculated. It is shown that these configurations, thanks to the cancellation of all unwanted terms, are responsible for the restoration of the perfect factorizability of the residue.