VERTEX CORRECTIONS IN GAUGE-THEORIES FOR 2-DIMENSIONAL CONDENSED MATTER SYSTEMS

We calculate the self-energy of two-dimensional fermions that are coup led to transverse gauge fields, taking two-loop corrections into accou nt. Given a bare gauge field propagator that diverges for small moment um transfers q as 1/q(eta), 1 < eta less than or equal to 2, the fermi onic self-energy without vertex corrections vanishes for small frequen cies omega as Sigma(omega) proportional to omega(gamma) with gamma = 2 /(1 + eta) < 1. We show that inclusion of the leading radiative correc tion to the fermion-gauge field vertex leads to Sigma(omega) proportio nal to omega(gamma)[1 - a(eta) ln(omega(0)/omega)], where a(eta) is a positive numerical constant and omega(0) is some finite energy scale. The negative logarithmic correction is consistent with the scenario th at higher order vertex corrections push the exponent gamma to larger v alues.