The chiral phase transition is investigated within the framework of the linear sigma model at finite temperature. We concentrate on the meson sector of the model and calculate the finite temperature effective potential in the Hartree approximation by using the Cornwall-Jackiw-Tomboulis formalism of composite operators. The effective potential is calculated for N = 4 involving the usual sigma and three pions and in the large N approximation involving N − 1 pion fields. In the N = 4 case we have examined the theory both in the chiral limit and with the presence of a symmetry breaking term which generates the pion masses. In both cases we have solved the system of the resulting gap equations for the thermal effective masses of the particles numerically and we have investigated the evolution of the effective potential. In the N = 4 case there is indication of a first order phase transition and the Goldstone theorem is not satisfied. The situation is different in the general case using the large N approximation, the Goldstone theorem is satisfied and the phase transition is of the second order. For this analysis we have ignored quantum effects and we used the imaginary time formalism for calculations.

The effect of finite isospin chemical potential to the effective masses of the mesons at finite temperature is investigated in the framework of the O(4) linear sigma model with explicit chiral symmetry breaking. We present a mechanism to include the isospin chemical potential in the model. By using the Cornwall-Jackiw-Tomboulis method of composite operators, we obtain a set gap equations for the effective masses of the mesons and get the numerical results in the Hartree approximation. We find that the introduction of the chemical potential only affects the mass of the charged pions and sigma, while there is almost NO effects on the mass of neutral pions.

It has been some time since an empirical relation, which correlates DC with AC conductivity and contains a loosely defined coefficient thought to be of order one, was introduced by Barton, Nakajima and Namikawa. In this work, we derived this relation assuming that the conductive response consists of a superposition of DC conductivity and an AC conductivity term which materialized through a HavriliakNegami dielectric function. The coefficient was found to depend on the Havriliak-Negami shape parameters as well as on the ratio of two characteristic time scales of ions motion which are related to ionic polarization mechanism and the onset of AC conductivity. The results are discussed in relation to other relevant publications and they also applied to a polymeric material. Both, theoretical predictions and experimental evaluations of the BNN coefficient are in an excellent agreement, while this coefficient shows a gradual reduction as the temperature increases.

Low-energy meson-meson scattering data are a powerful testing ground for quark models. Here, we describe the behaviour at threshold of S-wave scattering-matrix singularities. The majority of the full scattering-matrix mesonic poles stem from an underlying confinement spectrum. However, the light scalar mesons K0*(830), a0(980), f0(400-1200), and f0(980) do not, but instead originate in 3P0-barrier semi-bound states. We show that the behaviour of the corresponding poles is identical at threshold. In passing, the light-meson sector is given a firm basis.Comment: Plain LaTeX, 16 pages Contribution to the Second International Workshop on Hadron Physics, Effective Theories of Low Energy QCD, 25-29 September, 2002 (Coimbra, Portugal

We have used the Cornwall-Jackiw-Tomboulis method of composite operators and its formulation at finite temperature by Amelino-Camelia and Pi, in order to calculate the effective potential of the O(4) linear sigma model beyond the Hartree approximation. We have obtained a system of gap equations for the effective mass of sigma and the pions as well as for the condensate, the order parameter of the chiral phase transition. We find that the thermal effective mass of the pions at low temperatures remains lower than in the Hartree case, nevertheless deviates from the chiral limit. Our observation is consistent with other results which have been published previously. * Contribution to the proceedings of the conference: X Hadron Physics and VII Relativistic Aspects of Nuclear Physics: A joint meeting on QCD and QGP, (