  In this thesis we present contributions in the field of the applications of
quantum field theories techniques to condensed matter models. In chapter 3 we
investigate on the non covariant fermionic determinant and its connection to
Luttinger liquids. We address the problem of the regularization of the theory.
In chapter 4 we treat spin flipping interactions in the non local Thirring
model and we obtain an effective bosonic actions that describe separated spin
and charge degrees of freedom. In chapter 4 we apply the self consistent
harmonic approximation to previously derived bosonic action and we obtain
potential depending equations for the spectrum gap. In chapter 5 we include
spin-orbit couplings and compute correlations functions. We show that the spin
orbit interactions modify the exponents and the phase diagram of the system and
makes new susceptibilities diverge for low temperature. Finally in chapter 6 we
summarize the main results and the conclusions.
