Baryon Density and the Dilated Chiral Quark Model
  We calculate perturbatively the effect of density on hadronic properties using the chiral quark model implemented by the QCD trace anomaly to see the possibility of constructing Lorentz invariant Lagrangian at finite density. We calculate the density dependent masses of the constituent quark, the scalar field and the pion in one-loop order using the technique of thermo field dynamics. In the chiral limit, the pion remains massless at finite density. It is found that the tadpole type corrections lead to the decreasing masses with increasing baryon density, while the radiative corrections induce Lorentz-symmetry-breaking terms. We found in the large $N_c$ limit with large scalar mass that the tadpoles dominate and the mean-field approximation is reliable, giving rise a Lorentz-invariant Lagrangian with masses decreasing as the baryon density increases. 
Youngman Kim and Hyun Kyu Lee