  The need for suitable many or infinite fermion correlation functions to
describe some low dimensional strongly correlated systems is discussed. This is
linked to the need for a correlated basis, in which the ground state may be
postive definite, and in which single particle correlations may suffice. A
particular trial basis is proposed, and applied to a certain quasi-1D model.
The model is a strip of the 2D square lattice wrapped around a cylinder, and is
related to the ladder geometries, but with periodic instead of open boundary
conditions along the edges. Analysis involves a novel mean-field approach and
exact diagonalisation. The model has a paramagnetic region and a Nagaoka
ferromagnetic region. The proposed basis is well suited to the model, and
single particle correlations in it have power law decay for the paramagnet,
where the charge motion is qualitatively hard core bosonic. The mean field also
leads to a BCS-type model with single particle long range order.
