High energy bosons do not propagate

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.