Instantons in Schwinger Model

Abstract

The known calculations of the fermion condensate $<\bar{\psi }\psi >$ and the correlator $<\bar{\psi }\psi (x)\bar{\psi }\psi (0)>$ 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 ${\mu }^{-1}$. At high temperature, these instantons become quasistatic and present the 2-dimensional analog of the `walls' found recently in 4-dimensional gauge theories. In spite of the static nature of these solutions, they should not be interpreted as `thermal solitons' 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 $QE{D}_2$ is saturated by the rarefied gas of instantons and antiinstantons with density $\propto m\exp \{-S^{inst.}\}=m\exp \{-\pi T/\mu \}$ to be confronted with the dense strongly correlated instanton-antiinstanton liquid saturating the partition function at $T=0$.

Santa Barbara Preprint NSF-ITP-93-151

References in corpus (4)

• Z(N) interface tension in a hot SU(N) gauge theory
• Mesonic Correlation Functions in the Random Instanton Vacuum
• Quark Propagation in the Random Instanton Vacuum
• Instantons and the Ground State of the Massive Schwinger Model

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