  We first describe a class of spinor-curvature identities (SCI) which have
gravitational applications. Then we sketch the topic of gravitational
energy-momentum, its connection with Hamiltonian boundary terms and the issues
of positivity and (quasi)localization. Using certain SCIs several spinor
expressions for the Hamiltonian have been constructed. One SCI leads to the
celebrated Witten positive energy proof and the Dougan-Mason quasilocalization.
We found two other SCIs which give alternate positive energy proofs and
quasilocalizations. In each case the spinor field has a different role. These
neat expressions for gravitational energy-momentum have much appeal. However it
seems that such spinor formulations just have no room for angular momentum;
which leads us to doubt that spinor formulations can really correctly capture
the elusive gravitational energy-momentum.
