  We present two novel relations between the quasiparticle interaction in
nuclear matter and the unique low momentum nucleon-nucleon interaction in
vacuum. These relations provide two independent constraints on the Fermi liquid
parameters of nuclear matter. Moreover, the new constraints define two
combinations of Fermi liquid parameters, which are invariant under the
renormalization group flow in the particle-hole channels. Using empirical
values for the spin-independent Fermi liquid parameters, we are able to compute
the major spin-dependent ones by imposing the new constraints as well as the
Pauli principle sum rules.
