  We use the recently introduced theory for the kinetics of systems of
classical particles to investigate systems driven by Smoluchowski dynamics. We
investigate the existence of ergodic-nonergodic (ENE) transitions near the
liquid-glass transition. We develop a self-consistent perturbation theory in
terms of an effective two-body potential. We work to second order in this
potential. At second order we have an explicit relationship between the static
structure factor and the effective potential. We choose the static structure
factor in the case of hard spheres to be given by the solution of the
Percus-Yevick approximation for hard spheres. Then using the analytically
determined ENE equation for the ergodicity function we find an ENE transition
for packing fraction, eta, greater than a critical value eta*=0.76 which is
physically unaccessible. The existence of a linear fluctuation-dissipation
theorem in the problem is shown and used to great advantage.
