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We calculate the Altshuler-Aronov type quantum correction to the conductivityof $2d$ charge carriers in a random potential (or random magnetic field)coupled to a transverse gauge field. The gauge fields considered simulate theeffect of the Coulomb interaction for the fractional quantum Hall state at halffilling and for the $t-J$ model of high-$T_c$ superconducting compounds. Wefind an unusually large quantum correction varying linearly or quadraticallywith the logarithm of temperature, in different temperature regimes.Comment: 12 pages REVTEX, 1 figure. The figure is added and minor misprints  are correcte

Quantum corrections to the conductivity of fermion gauge-field models: Application to the half-filled Landau level