  We discuss the propagation of bosons (scalars, gauge fields and gravitons) at
high energy in the context of the spectral action. Using heat kernel
techniques, we find that in the high-momentum limit the quadratic part of the
action does not contain positive powers of the derivatives. We interpret this
as the fact that the two point Green functions vanish for nearby points, where
the proximity scale is given by the inverse of the cutoff.
