Is the Exponential of the Chern-Simons Action a Normalizable Physical   State?
  We determine the wavefunction that corresponds to the exponential of the Chern-Simons action in a family of gravitational models provided with cosmological constant whose non-perturbative canonical quantization is completely known. We show that this wavefunction does not represent a proper quantum state, because it is not normalizable with respect to the unique inner product of Lorentzian gravity. 
Guillermo A. Mena Marugan