  We reconsider the theory of the half-filled Landau level with impurities
using the Chern-Simons formulation and study Ward identities for the
Chern-Simons theory. From these we get conductivity diagrams with impurities
which obey the continuity equation. We calculate the conductivity of these
diagrams for which we obtain log(T\tau) divergent conductivity diagrams for low
temperature T. We compare our result with the experimental values of the low
temperature conductivities. Finally we calculate the conductivity for small
deviations of the magnetic field B from the value nu=1/2. In this case we get a
singularity in the conductivity.
