Auxiliary Field Meson Model at Finite Temperature and Density

Starting from many quark interactions, we construct a nonlinear sigma-omega model at finite temperature and density. The mesons are introduced as auxiliary fields. Effective quark-meson couplings are strongly related to effective meson masses, since they are derived simultaneously from the original many quark interactions. In this model, even if the effective omega-meson mass decreases due to the partial chiral restoration, the equation of state (EOS) of nuclear matter can become soft.