  The wavefunction renormalization in the Hubbard model is studied, by using
well tested mean field tecniques. The 'orthogonality catastrophe' is shown to
exist, even in 2D, for doping levels sufficiently close to half filling. The
results are extended beyond mean field, by constructing delocalized
wavefunctions, with the correct symmetries of the exact solutions. The physics
are still well described by the assumption of the existence of the
orthogonality catastrophe.
