  The classical formalism of the Moment Problem has been combined with a
cumulant approach and applied to the extensive many-body problem. This has
yielded many new exact results for many-body systems in the thermodynamic limit
- for the ground state energy, for excited state gaps, and for arbitrary ground
state averages. The method applies to any extensive Hamiltonian system, for any
phase or symmetry arising in the model, whether on a lattice or in the
continuum, and for any dimensionality. The theorems are of a nonperturbative
nature with respect to any couplings occuring in the model.
