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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 behaviour 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.