  The Hartle-Hawking wave function is known to be the Fourier dual of the
Chern-Simons or Kodama state reduced to mini-superspace, using an integration
contour covering the whole real line. But since the Chern-Simons state is a
general solution of the Hamiltonian constraint (with a given ordering), its
Fourier dual should provide the general solution (i.e. beyond mini-superspace)
of the Wheeler DeWitt equation representing the Hamiltonian constraint in the
metric representation. We write down a formal expression for such a wave
function, to be seen as the generalization beyond mini-superspace of the
Hartle-Hawking wave function. Its explicit evaluation (or simplification)
depends only on the symmetries of the problem, and we illustrate the procedure
with anisotropic Bianchi models and with the Kantowski-Sachs model. A
significant difference of this approach is that we may leave the torsion inside
the wave functions when we set up the ansatz for the connection, rather than
setting it to zero before quantization. This allows for quantum fluctuations in
the torsion, with far reaching consequences.
