We discuss renormalization group approaches to strongly interacting Fermi systems, in the context of Landaus theory of Fermi liquids and functional methods, and their application to neutron matter.
We show that microscopic calculations based on chiral effective field theory interactions constrain the properties of neutron-rich matter below nuclear densities to a much higher degree than is reflected in commonly used equations of state. Combined
with observed neutron star masses, our results lead to a radius R = 9.7 - 13.9 km for a 1.4 M_{solar} star, where the theoretical range is due, in about equal amounts, to uncertainties in many-body forces and to the extrapolation to high densities.
