  We present a first step toward a microscopic theory for the glass transition
in systems with trivial static correlations. As an example we have chosen N
infinitely thin hard rods with length L, fixed with their centers on a periodic
lattice with lattice constant a. Starting from the N-rod Smoluchowski equation
we derive a coupled set of equations for fluctuations of reduced k-rod
densities. We approximate the influence of the surrounding rods onto the
dynamics of a pair of rods by introduction of an effective rotational diffusion
tensor D and in this way we obtain a self-consistent equation for D. This
equation exhibits a feedback mechanism leading to a slowing down of the
relaxation. It involves as an input the Laplace transform v_0(l/r) at z=0,
l=L/a, of a torque-torque correlator of an isolated pair of rods with distance
R=ar. Our equation predicts the existence of a continuous ergodicity-breaking
transition at a critical length l_c=L_c/a. To estimate the critical length we
perform an approximate analytical calculation of v_0(l/r) based on a
variational approach and obtain l_c^{var}=5.68, 4.84 and 3.96 for an sc, bcc
and fcc lattice. We also evaluate v_0(l/r) numerically exactly from a two-rod
simulation. The latter calculation leads to l_c^{num}=3.45, 2.78 and 2.20 for
the corresponding lattices. Close to l_c the rotational diffusion constant
decreases as D(l) ~ (l_c - l)^\gamma with \gamma=1 and a diverging time scale
t_\epsilon ~ |l_c - l|^{-\delta}, \delta=2, appears. On this time scale the t-
and l-dependence of the 1-rod density is determined by a master function
depending only on t/t_\epsilon. In contrast to present microscopic theories our
approach predicts a glass transition despite the absence of any static
correlations.
