Quenched massive Schwinger model in the infrared approximation.

Abstract

In the quenched, continuum version of the Schwinger model, a gauge-invariant summation over soft photons exchanged across a fermion loop is performed for the order parameter 〈\ensuremath{\psi}\ifmmode\bar\else\textasciimacron\fi{} \ensuremath{\psi}〉 and the correlation function 〈\ensuremath{\psi}\ifmmode\bar\else\textasciimacron\fi{} \ensuremath{\psi}(x) \ensuremath{\psi}\ifmmode\bar\else\textasciimacron\fi{} \ensuremath{\psi}(y)〉 with a fermion mass m\ensuremath{\ne}0 and photon momentum k<m. The limit m\ensuremath{\rightarrow}0 leads to a finite, nonzero value for 〈\ensuremath{\psi}\ifmmode\bar\else\textasciimacron\fi{} \ensuremath{\psi}〉; in the correlation function the leading terms, proportional to 〈\ensuremath{\psi}\ifmmode\bar\else\textasciimacron\fi{} \ensuremath{\psi}${〉}^{2}$, cancel between the two types of diagrams leaving free massless propagation.