We consider the Hubbard model and its extensions on bipartite lattices
. We define a dynamical group based on the eta-pairing operators intro
duced by Yang, and define coherent pairing states, which are combinati
ons of eigenfunctions of eta-operators. These states permit exact calc
ulations of numerous physical properties of the system, including ener
gy, various fluctuations and correlation functions, including pairing
off-diagonal long-range order to all orders. This approach is compleme
ntary to BCS, in that these are superconducting coherent states associ
ated with the exact model, although they are not eigenstates of the Ha
miltonian.