Non-Abelian gauge invariance and the infrared approximation

Two constructions are given of infrared approximations, defined by a nonlocal configuration-space restrictions, which preserve the local, non-Abelian gauge invariance of SU(N) two-dimensional QCD (${\mathrm{QCD}}_2$). These continuum infrared methods are used to estimate the quenched order parameter 〈ψ¯ψ〉 in the strong-coupling, or chiral, limit and are compared to a previous calculation where gauge invariance was not manifest. Both constructions provide results which, in the chiral limit, differ from each other and from the previous estimation by an inessential, multiplicative scaling factor.