  We consider the quantum corrections to the conductivity of fermions
interacting via a Chern-Simons gauge field, and concentrate on the Hartree-type
contributions. The first-order Hartree approximation is only valid in the limit
of weak coupling \lambda to the gauge field, and results in an antilocalizing
conductivity correction, \sim \lambda^2 g \ln^2 T (g is the conductance). In
the case of strong coupling, an infinite summation of higher-order terms is
necessary, including both the virtual (renormalization) and real (dephasing)
processes. At intermediate temperatures 1/g^2\tau<<T<<1/g\tau (\tau is the
transport time), the T-dependence of the conductivity is determined by the
Hartree correction. At low temperatures T<<1/g^2\tau, the Hartree correction
assumes a logarithmic form with a coefficient of order unity. As a result, the
negative exchange contribution becomes dominant, yielding localization in the
limit of zero T. We further discuss dephasing at strong coupling and show that
the dephasing rates are of the order of T, owing to the interplay of inelastic
scattering and renormalization. On the other hand, the dephasing length is
anomalously short, L_\phi<<L_T. For the case of composite fermions with
long-range Coulomb interaction, the Hartree correction has the usual
T-dependence, and for realistic g is overcompensated by the negative exchange
contribution due to the gauge-boson and scalar parts of the interaction. In
this case, the dephasing length L_\phi is of the order of L_T for not too low T
and exceeds L_T for T<1/g\tau.
