  This thesis report deals with the 1D Hubbard model and the quantum objects
that diagonalize the normal ordered Hubbard hamiltonian, among those the so
called PseudoFermions (PFs). These PFs have no residual energy interactions,
are eta-spin and spin zero objects, and are the scatterers and the scattering
centers of the theory. The S-matrix of this representation is a simple phase
factor, involving the phase shifts of the zero energy forward momentum
scattering events.
  A PF dynamical theory is developed and applied to the one-electron removal
and lower Hubbard band addition cases. For any value of the on-site effective
Coloumb repulsion and electronic density, and in the limit of zero
magnetization, we derive closed form expressions for these spectral functions,
showing the emergence of the power-law type behavior of correlation functions
of Luttinger liquids. However, our expressions are valid for the entire
elementary excitation energy bandwidth.
  The singular behavior of the theoretical spectral weight leads to a spectral
weight distribution detectable by photo emission and photo absorption
experiments. As an important contribution to the understanding of quasi 1D
materials, we are able to reproduce for the whole energy bandwidth, the
experimental spectral distributions recently found for the organic compound
TTF-TCNQ. This confirms the validity of the PF dynamical theory, and provides a
deeper understanding of low dimensional correlated systems.
