For an asymptotically flat initial-data set in general relativity, the total
mass-momentum may be interpreted as a Hermitian quadratic form on the complex,
two-dimensional vector space of ``asymptotic spinors''. We obtain a
generalization to an arbitrary initial-data set. The mass-momentum is retained
as a Hermitian quadratic form, but the space of ``asymptotic spinors'' on which
it is a function is modified. Indeed, the dimension of this space may range
from zero to infinity, depending on the initial data. There is given a variety
of examples and general properties of this generalized mass-momentum.Comment: 25 pages, LaTe