Microscopic theory for the glass transition in a system without static correlations

We study the orientational dynamics of infinitely thin hard rods of length L, with the centers-of-mass fixed on a simple cubic lattice with lattice constant a.We approximate the influence of the surrounding rods onto dynamics of a pair of rods by introducing an effective rotational diffusion constant D(l),l=L/a. We get D(l) ~ [1-v(l)], where v(l) is given through an integral of a time-dependent torque-torque correlator of an isolated pair of rods. A glass transition occurs at l_c, if v(l_c)=1. We present a variational and a numerically exact evaluation of v(l).Close to l_c the diffusion constant decreases as D(l) ~ (l_c-l)^\gamma, with \gamma=1. Our approach predicts a glass transition in the absence of any static correlations, in contrast to present form of mode coupling theory.