Analytic Method to Study Influence of Finite Chemical Potential in QED_3~*

Adopting the approximation to the first order of chemical potential μ, we resolve rigidly the influence on fermion condensate from μ in QED3. We show that this condensate does not respond linear expression to μ. Moreover, the influence on fermion chiral condensate from chemieal potential is investigated.

Fermion-Boson Vertex at Finite Chemical Potential

Based on the Ward-Takahashi identity at finite chemical potential and Lorentz structure analyms, we generalize the Ball-Chiu vertex to the case of nonzero chemical potential and obtain the general form of the frmionboson vertex in QED at finite chemical potential.

A Model-Independent Discussion of Quark Number Density and Quark Condensate at Zero Temperature and Finite Quark Chemical Potential

Generally speaking, the quark propagator is dependent on the quark chemical potential in the dense quantum chromodynamics （QCD）. By means of the generating functional method, we prove that the quark propagator actually depends on p4 ＋ iμ from the first principle of QCD. The relation between quark number density and quark condensate is discussed by analyzing their singularities. It is concluded that the quark number density has some singularities at certain # when T = 0, and the variations of the quark number density as well as the quark condensate are located at the same point. In other words, at a certain # the quark number density turns to nonzero, while the quark condensate begins to decrease from its vacuum value.

Linear Chemical Potential Dependence of Two-Quark Condensate

By differentiating the inverse dressed quark propagator at finite chemical potential μ with respect to μ, the linear response of the dressed quark propagato r to the chemical potential can be obtained, From this we extract a modelindependent formula for the linear chemical potential dependence of the in-medium two-quark condensate and show by two independent methods （explicit calculation and Lorentz covariance arguments） that the first-order contribution in μ to the in-medium two-quark condensate vanishes identically. Therefore if one wants to study the in-medium two-quark condensate one should expand to at/east the second order in the chemical potential μ.

Chemical Potential Dependence of Vertices

Based on the rainbow-ladder approximation of the Dyson-Schwinger equations and the assumption of the analyticity of the fermion-boson vertex in the neighborhood of zero chemical potential （μ = 0） and neglecting the #-dependence of the dressed gluon propagator, we apply the method in [Phys. Rev. C 71 （2005） 015205] of studying the dressed quark propagator at finite chemical potential to prove that the general fermion-boson vertex at finite μ can also be obtained from the one at μ = 0 by a simple shift of variables. Using this result we extend the results of [Phys. Lett. B 420 （1998） 267] to the situation of finite chemical potential and show that under the approximations we have taken, the Gell-Mann Oakes-Renner relation also holds at finite chemical potential

QCD phase diagram at finite isospin chemical potential and temperature in an IR-improved soft-wall AdS/QCD model

We study the phase transition between the pion condensed phase and normal phase,as well as chiral phase transition in a two flavor(Nf=2)IR-improved soft-wall AdS/QCD model at finite isospin chemical potentialμI and temperature T.By self-consistently solving the equations of motion,we obtain the phase diagram in the plane ofμI and T.The pion condensation appears together with a massless Nambu-Goldstone boson mπ1(Tc,μcI)=0,which is very likely to be a second-order phase transition with mean-field critical exponents in the smallμI region.When T=0,the critical isospin chemical potential approximates to vacuum pion massμcI≈m0.The pion condensed phase exists in an arched area,and the boundary of the chiral crossover intersects the pion condensed phase at a tri-critical point.Qualitatively,the results are in good agreement with previous studies on lattice simulations and model calculations.

Pion properties at finite isospin chemical potential with isospin symmetry breaking

Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU（2） NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI 〈 0 and μI 〉0 in the phase diagram, and different values for the charged pion mass（or decay constant） and neutral pion mass（or decay constant） at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses.