  Renormalization group methods can be applied to the nuclear many-body problem
using the approach proposed by Shankar. We start with the two-body low momentum
interaction V_{low k} and use the RG flow from the particle-hole channels to
calculate the full scattering amplitude in the vicinity of the Fermi surface.
This is a new straightforward approach to the many-body problem which is
applicable also to condensed matter systems without long-range interactions,
such as liquid 3He. We derive the one-loop renormalization group equations for
the quasiparticle interaction and the scattering amplitude at zero temperature.
The RG presents an elegant method to maintain all momentum scales and preserve
the antisymmetry of the scattering amplitude. As a first application we solve
the RG equations for neutron matter. The resulting quasiparticle interaction
includes effects due to the polarization of the medium, the so-called induced
interaction of Babu and Brown. We present results for the Fermi liquid
parameters, the equation of state of neutron matter and the 1S0 superfluid
pairing gap.
