Effective Field Theories For Nuclei And Dense Matter

A recent development on the working of effective field theories in nuclei and in dense hadronic matter is discussed. We consider two extreme regimes: One, dilute regime for which fluctuations are made on top of the matter-free vacuum; two, dense systems for which fluctuations are treated on top of the "vacuum" defined at a given density, with masses and coupling constants varying as function of matter density ("Brown-Rho scaling"). Based on an intricate -- as yet mostly conjectural -- connection between the in-medium structure of chiral Lagrangian field theory which is a beautiful effective theory of QCD and that of Landau Fermi liquid theory which is an equally beautiful and highly successful effective theory of many-body systems, it is suggested that a chiral Lagrangian with Brown-Rho scaling in the mean field is equivalent to Fermi-liquid fixed point theory. I make this connection using electroweak and strong responses of nuclear matter up to nuclear matter density and then extrapolating to higher densities encountered in heavy-ion collisions and compact stars.