(Mis-)handling gauge invariance in the theory of the quantum Hall effect. II. Perturbative results

The concept of F invariance, which previously arose in our analysis of the integral and half-integral quantum Hall effects, is studied in 2+2ε spatial dimensions. We report the results of a detailed renormalization-group analysis, and establish the renormalizability of the (Finkelstein) action to two-loop order. We show that the infrared behavior of the theory can be extracted from gauge-invariant (F-invariant) quantities only. For these quantities (conductivity, specific heat) we derive explicit scaling functions. We identify a bosonic quasiparticle density of states which develops a Coulomb gap as one approaches the metal-insulator transition from the metallic side. We discuss the consequences of F invariance for the strong-coupling, insulating regime.