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.

Abstract. With the linear sigma model, we have studied Bose-Einstein condensation and the chiral phase transition in the chiral limit for an interacting pion system. A µ − T phase diagram including these two phenomena is presented. It is found that the phase plane has been divided into three areas: the Bose-Einstein condensation area, the chiral symmetry broken phase area and the chiral symmetry restored phase area. Bose-Einstein condensation can happen either from the chiral symmetry broken phase or from the restored phase. We show that the onset of the chiral phase transition is restricted in the area where there is no Bose-Einstein condensation.

The BEC of charged pions is investigated in the framework of O(4) linear sigma model. By using Cornwall-Jackiw-Tomboulis formalism, we have derived the gap equations for the effective masses of the mesons at finite temperature and finite isospin density. The BEC is discussed in chiral limit and non-chiral limit at Hartree approximation and also at large N approximation.

We have studied the chiral soliton model in a thermal vacuum. The soliton equations are solved at finite temperature and density. The temperature or density dependent soliton solutions are presented. The physical properties of baryons are derived from the soliton solutions at finite temperature and density. The temperature or density dependent variation of the baryon properties are discussed.

We have attempted to apply the CJT formalism to study the nuclear matter. The thermodynamic potential is calculated in Hartree-Fock approximation in the CJT formalism. After neglecting the medium effects to the mesons, the numerical results are found very consistent with those obtained from the mean field calculation. In our calculation the thermodynamical consistency is also preserved.

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In the mean-field approximation, we have studied the soliton which is embedded in a thermal medium within the chiral soliton model. The energy of the soliton or the baryon mass in the thermal medium has been carefully evaluated, in which we emphasize that the thermal effective potential in the soliton energy should be properly treated in order to derive a finite and well-defined baryon mass out of the thermal background. The result of the baryon mass at finite temperatures and densities in chiral soliton model are clearly presented.

I have used a practical method to calculate the one-loop quantum correction to the energy of the non-topological soliton in Friedberg-Lee model. The quantum effects which come from the quarks of the Dirac sea scattering with the soliton bag are calculated by a summation of the discrete and continuum energy spectrum of the Dirac equation in the background field of soliton. The phase shift of the continuum spectrum is numerically calculated in an efficient way and all the divergences are removed by the same renormalization procedure.PACS numbers: 11.10. Gh, 11.15.Kc, 11.27.+d, 12.39.Ba Non-topological soliton models which are effective models inspired from the underlying QCD theory are phenomenologically successful in describing the low energy nuclear physics. However, the main calculation methods in these models are based on mean field approximation, in other words treating the fields classically [1][2][3][4]. The quantum corrections in the background fields of spatially non-trivial configurations are very difficult to calculate. This is partly due to the fact that these calculations are nonlocal. During the past decades different calculation methods and approximate schemes have been developed on this problem [5][6][7][8][9][10][11][12]. As the calculation of quantum corrections of solitons is much more complex than those usual calculations of quantum loop corrections of trivial background fields, most studies on this problem are based on the derivative expansion method [5][6][7][8][9]. The renormalization in this method is a very nontrivial task. One remarkable calculation method was that developed by Farhi, Graham, Haagensen and Jaffe [13]. It is a systematic and efficient scheme for calculating the quantum corrections about static field configuration in renormalizable field theories, in which all the divergences are removed by the same renormalization procedure. As originally this method was applied in the Higggs like models and the main interest was focused on studying solitons in the standard electroweak models [13,14], there are no applications of this method, as far as I know, in strong interaction hadronic models, like the FriedbergLee(FL) model, the linear sigma model and other QCD effective models. In recent years topological solitons in strong interaction QCD theory have drawn lots of attentions [15,16]. One needs an efficient method to calculate the quantum correction of the soliton in effective QCD theories [17]. So in this paper as the first small step I want to introduce this method to calculate the one loop quantum fluctuation of the non-topological soliton in the FL model. In this method one makes the energy level summation by calculating the discrete and continuous energy spectrum and the continuum contribution is determined through evaluating scattering phase shift in a concise way. The renormalization of the field configuration energy could be done in a manner consistent with on-shell mass and coupling constant renormalization in the perturbative sector. Comparing to the precedent calculati...