Instantons in Schwinger Model

Abstract

The known calculations of the fermion condensate $<\barψψ>$ and the correlator $<\barψψ(x) ~\barψψ(0)>$ have been interpreted in terms of {\em localized} instanton solutions minimizing the {\em effective} action. Their size is of order of massive photon Compton wavelength $μ^{-1}$. At high temperature, these instantons become quasistatic and present the 2-dimensional analog of the `walls&#39; found recently in 4-dimensional gauge theories. In spite of the static nature of these solutions, they should not be interpreted as `thermal solitons&#39; living in Minkowski space: the mass of these would-be solitons does not display itself in the physical correlators. At small but nonzero fermion mass, the high-T partition function of $QED_2$ is saturated by the rarefied gas of instantons and antiinstantons with density $\propto m~\exp\{-S^{inst.}\}~=~m~\exp\{-πT/μ\}$ to be confronted with the dense strongly correlated instanton-antiinstanton liquid saturating the partition function at $T=0$.