  In this thesis, we study the breakdown of the Fermi liquid state in cuprate
superconductors using the renormalization group (RG). We seek to extend earlier
work on the crossover from the Fermi liquid state to the pseudo gap phase based
on RG flows in the so-called saddle point regime. Progress in the derivation of
effective models for the conjectured spin liquid state has been hindered, by
the difficulties involved in solving the strong coupling low energy
Hamiltonian. We tackle the problem by introducing an orthogonal wave packet
basis, the so-called Wilson-Wannier (WW) basis, that can be used to interpolate
between the momentum space and the real space descriptions.
  We show how to combine the WW basis with the RG, such that the RG is used to
eliminate high-energy degrees of freedom, and the remaining strongly correlated
system is solved approximately in the WW basis. We exemplify the approach for
different one-dimensional model systems, and find good qualitative agreement
with exact solutions even for very simple approximations.
  Finally, we reinvestigate the saddle point regime of the two-dimensional
Hubbard model. We show that the anti-nodal states are driven to an insulating
spin-liquid state with strong singlet pairing correlations, thus corroborating
earlier conjectures.
