  In the Einstein-Cartan framework the torsion-free conditions arise within the
Hamiltonian treatment as second-class constraints. The standard strategy is to
solve these constraints, eliminating the torsion from the classical theory,
before quantization. Here we advocate leaving the torsion inside the other
constraints before quantization, leading at first to wave functions that can be
called ``kinematical'' with regards to the torsion, but not the other
constraints. The torsion-free condition can then be imposed as a condition upon
the physical wave packets one constructs, satisfying the usual uncertainty
relations, and so with room for quantum fluctuations in the torsion. This
alternative strategy has the surprising effect of clarifying the sense in which
the wave functions solving an explicitly real theory are ``delta-function
normalizable''. Such solutions with zero (or any fixed) torsion, should be
interpreted as plane waves in torsion space. Properly constructed wave packets
are therefore normalizable in the standard sense. Given that they are canonical
duals, this statement applies equally well to the Chern-Simons state
(connection representation) and the Hartle-Hawking wave function (metric
representation). We show how, when torsion is taken into account, the
Hartle-Hawking wave function is replaced by a Gauss-Airy function, with finite
norm, which we call the Hartle-Hawking beam. The Chern-Simons state, instead,
becomes a packet with a Gaussian probability distribution in connection space.
We conclude the paper with two sections explaining how to generalize these
results beyond minisuperspace.
