Quark condensate in nuclear matter based on Nuclear Schwinger-Dyson   formalism
  The effects of higher order corrections of ring diagrams for the quark condensate are studied by using the bare vertex Nuclear Schwinger Dyson formalism based on $\sigma$-$\omega$ model. At the high density the quark condensate is reduced by the higher order contribution of ring diagrams more than the mean field theory or the Hartree-Fock . 
Tomohiro Mitsumori, Nobuo Noda, Hiroaki Kouno, Akira Hasegawa and   Masahiro Nakano