Theory of polarized Fermi liquid

The dispersion law of transverse spin waves known in the Stoner-Hubbard model of itinerant ferromagnetism corresponds to that is well known in more broder and well controlled approach of Fermi-liquid theory. Making use the quantum-field theoretical approach we derive the dispersion law for the transverse spin waves in a weakly polarized Fermi liquid at T=0. Along with the dissipationless part inversely proportional to the polarization it contains also the finite zero-temperature damping. It is shown that similar derivation for "ferromagnetic Fermi liquid" taking into consideration the divergency of static transverse susceptibility also leads to the same attenuating spin wave spectrum. Hence, in both cases we deal in fact with spin polarized Fermi liquid but not with isotropic itinerant ferromagnet where the zero temperature atenuation is prohibited by Goldstone theorem. It demonstrates, the troubles of the Fermi liquid formulation of a theory of itinerant ferromagnetic systems.