  The eigenvalue problem for the Sen--Witten operator on closed spacelike
hypersurfaces is investigated. The (square of its) eigenvalues are shown to be
given exactly by the 3-surface integral appearing in the expression of the
total energy-momentum of the matter+gravity systems in Witten's energy
positivity proof. A sharp lower bound for the eigenvalues, given in terms of
the constraint parts of the spacetime Einstein tensor, i.e. the energy and
momentum densities of the matter fields, is given.
