Spin waves in superfluidHe3: Collisionless regime

Spin waves in superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are studied in the collisionless regime by introducing a canonical transformation in the kinetic equation for the distribution-function matrix. This transformation is a space-time—dependent spin rotation, which takes into account the fluctuations of the direction of the order parameter which are coupled to the spin-density fluctuations. After the transformation, the order parameter is invariant. The kinetic equation is then expanded to lowest order in $\omega$ and $\overrightarrow{\mathrm{q}}$ and diagonalized. Fermi-liquid effects are taken into account. The result is a set of equations describing the coupled motion of the superfluid parameters and the quasiparticle distribution. In the axial state, only two degenerate spin-wave modes exist. These have their spin polarization perpendicular to the direction of the order parameter in spin space. In the isotropic state, one longitudinal and two transverse modes are obtained. Equations giving the velocity of these modes are written.