  We evaluate the spin polarization (Edelstein or inverse spin galvanic effect)
and the spin Hall current induced by an applied electric field by including the
weak localization corrections for a two-dimensional electron gas. We show that
the weak localization effects yield logarithmic corrections to both the spin
polarization conductivity relating the spin polarization and the electric field
and to the spin Hall angle relating the spin and charge currents. The
renormalization of both the spin polarization conductivity and the spin Hall
angle combine to produce a zero correction to the total spin Hall conductivity
as required by an exact identity. Suggestions for the experimental observation
of the effect are given.
