BRS Cohomology of a Bilocal Model

We present a model in which a gauge symmetry of a field theory is intrinsic in the geometry of an extended space time itself. A consequence is that the dimension of our space time is restricted through the BRS cohomology. If the Hilbert space is a dense subspace of the space of all square integrable $C^{\infty}$ functions, the BRS cohomology classes are nontrivial only when the dimension is two or four.