Schwinger Model Green functions with topological effects

TL;DR

This paper explicitly calculates fermion propagators and 4-fermion Green functions in massless QED2, incorporating topological effects and instanton sectors, revealing their impact on Green functions and quark condensates.

Contribution

It provides explicit solutions for Green functions in massless QED2 with topological effects, including instanton sectors, and analyzes their influence on physical quantities like quark condensates.

Findings

Green functions include topological instanton contributions

Quark condensates satisfy cluster property

Green functions' theta-dependence can be gauge-transformed away

Abstract

The fermion propagator and the 4-fermion Green function in the massless QED2 are explicitly found with topological effects taken into account. The corrections due to instanton sectors k=+1,-1, contributing to the propagator, are shown to be just the homogenous terms admitted by the Dyson-Schwinger equation for S. In the case of the 4-fermion function also sectors k=+2,-2 are included into consideration. The quark condensates are then calculated and are shown to satisfy cluster property. The theta-dependence exhibited by the Green functions corresponds to and may be removed by performing certain chiral gauge transformation.