  This paper addresses the question of whether Witten's proof of positive ADM
energy for classical general relativity can be extended to give a proof of
positive energy for a non-perturbative quantization of general relativity. To
address this question, a set of conditions is shown to be sufficient for
showing the positivity of a Hamiltonian operator corresponding to the ADM
energy. One of these conditions is a particular factor ordering for the
constraints of general relativity, in a representation where the states are
functionals of the Ashtekar connection, and the auxiliary, Witten spinor.
  These developments are partly based on results derived with Artem
Starodubtsev (unpublished notes, 2004).
