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.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.

arXiv:cond-mat/0405054May 4, 20040 citations

Non-local Thirring model at finite temperature

M. V. Manías, Carlos Naón, Marta L. Trobo

arXiv:hep-th/9712210Nuclear Physics BAug 1, 19988 citations

Nonlocal Currents as Coordinates for Particles

Josip Z. Soln

We investigate the possibility of formulating the dynamical theories in terms of nonlocal "currents." As an example, we formulate the nonrelativistic system of $n$ identical particles (with and without spin). From these models we learn that the extension to relativistic systems is possible. This is illustrated by treating the Thirring model in terms of nonlocal currents.We investigate the possibility of formulating the dynamical theories in terms of nonlocal "currents." As an example, we formulate the nonrelativistic system of $n$ identical particles (with and without spin). From these models we learn that the extension to relativistic systems is possible. This is illustrated by treating the Thirring model in terms of nonlocal currents.

Physical ReviewJul 25, 19683 citations

We investigate the possibility of formulating the dynamical theories in terms of nonlocal "currents." As an example, we formulate the nonrelativistic system of

n

identical particles (with and without spin). From these models we learn that the extension to relativistic systems is possible. This is illustrated by treating the Thirring model in terms of nonlocal currents.