Higher-order corrections in (2+1)-dimensional QED

Abstract

QED in 2+1 dimensions, analyzed to lowest order in the 1/N expansion, has been shown to exhibit dynamical chiral-symmetry breaking when the number N of fermions is less than 32/${\mathrm{\pi }}^2$. This analysis is extended by considering higher-order corrections to the gap equation. It is shown that while these corrections modify the form of the gap equation, the nature of the symmetry breaking remains the same. It is also shown that the critical number of fermions is a gauge-invariant quantity.