Spin dynamics of a Fermi liquid in an electric field

The influence of an external electric field on the spin dynamics of an elec trically neutral Fermi liquid is considered, the mechanism of such an influ ence being the relativistic spin-orbital interaction. As a result, Leggett 's equations for the spin dynamics of weakly polarized Fermi liquids are ge neralised to the case of non-zero external electric field. In addition, we obtained the transverse spin dynamics equation for strongly spin-polarized liquids in an electric field at zero temperature. In both situations covari ant derivatives depending on the electric field are shown to be substituted for spatial gradients in line with the SU(2) gauge invariance of the micro scopic Hamliltonian. The new equations are applied to the study of spin flo w along a channel, where an electric field is found to bring about an addit ional phase shift of thc order of magnitude of the phase shift in superflui d He-3 -B but growing with time.