Thermodynamic Bethe Ansatz for a family of scattering theories with U_q(sl(2)) symmetry

In this thesis work we analyze a wide class of 1+1 dimensional integrable scattering theories with Uq(sl(2)) quantum group symmetry, whose asymptotic states are multiplets of particles with iso-spin k/2. Their two-body S-matrices have been recently found in terms of the R matrix of the quantum group. Since they satisfy Yang-Baxter equation, unitarity and crossing symmetry, they represent a consistent integrable factorized scattering theory. The question of finding the corresponding underlying QFT can be addressed once the Thermodynamic Bethe Ansatz (TBA) is obtained. In this work we get the TBA equations and we compare them to previous known results of S. R. Aladim e M. J. Martins for the particular case when q→1.