  We quantize the generators of the little subgroup of the asymptotic
Poincar\'e group of Lorentzian four-dimensional canonical quantum gravity in
the continuum. In particular, the resulting ADM energy operator is densely
defined on an appropriate Hilbert space, symmetric and essentially
self-adjoint. Moreover, we prove a quantum analogue of the classical positivity
of energy theorem due to Schoen and Yau. The proof uses a certain technical
restriction on the space of states at spatial infinity which is suggested to us
given the asymptotically flat structure available. The theorem demonstrates
that several of the speculations regarding the stability of the theory,
recently spelled out by Smolin, are false once a quantum version of the
pre-assumptions underlying the classical positivity of energy theorem is
imposed in the quantum theory as well. The quantum symmetry algebra
corresponding to the generators of the little group faithfully represents the
classical algebra.
