Instantons and the infrared behavior of the fermion propagator in the Schwinger Model

TL;DR

This paper investigates the infrared behavior of the fermion propagator in the Schwinger Model, analyzing instanton sectors and gauge invariance, revealing exponential decay in certain gauge-invariant propagators and the influence of gauge choices.

Contribution

It provides a detailed analysis of the fermion propagator's infrared behavior in the Schwinger Model across different instanton sectors and gauges, including the exponential decay in path-dependent propagators.

Findings

Exponential dependence established for straight-line path propagators.

Leading behavior nearly identical across instanton sectors, differing by algebraic factors.

Gauge invariant dressed fermion amplitude can be reduced to gauge variant form in Landau gauge.

Abstract

Fermion propagator of the Schwinger Model is revisited from the point of view of its infrared behavior. The values of anomalous dimensions are found in arbitrary covariant gauge and in all contributing instanton sectors. In the case of a gauge invariant, but path dependent propagator, the exponential dependence, instead of power law one, is established for the special case when the path is a straight line. The leading behavior is almost identical in any sector, differing only by the slowly varying, algebraic prefactors. The other kind of the gauge invariant function, which is the amplitude of the dressed Dirac fermions, may be reduced, by the appropriate choice of the dressing, to the gauge variant one, if Landau gauge is imposed.