A Mean-Field Treatment in Studying Nuclear Matter Through a Thermodynamic Consistent Resummation Scheme

We used the Cornwall, Jackiw and Tomboulis (CJT) resummation scheme to study nuclear matter. In the CJT formalism the meson propagators are treated as the bare propagators and the the higher order loop corrections of the thermodynamic potential are evaluated at the Hartree approximation, while the vacuum fluctuations are ignored. Under these treatments in the CJT formalism we derived exact mean-field theory (MFT) results for the nuclear matter. The results are thermodynamically consistent, and our study indicates that the MFT result is the lowest order resummation result in the CJT resummation scheme. The relation between CJT formalism and MFT is clearly presented through the calculations.