Effective Field Theories, Landau-Migdal Fermi-Liquid Theory and Effective Chiral Lagrangians for Nuclear Matter

We reinterpret Landau-Migdal Fermi-liquid theory of nuclear matter as an effective chiral field theory with a Fermi surface. The effective field theory is formulated in terms of a chiral Lagrangian with its {\it mass and coupling parameters} scaling a la Brown-Rho and with the Landau-Migdal parameters identified as the fixed points of the field theory. We show how this mapping works out for response functions to the EM vector current and then using the same reasoning, make prediction on nuclear axial current, in particular on the enhanced axial-charge transitions in heavy nuclei. We speculate on how to extrapolate the resulting theory which appears to be sound both theoretically and empirically up to normal nuclear matter density $\rho_0$, to hitherto unexplored higher density regime relevant to relativistic heavy-ion processes and to cold compact (neutron) stars.