Microscopic modes in a Fermi superfluid. I. Linearized kinetic equations

This is the first of two papers in which microscopic expressions for the amplitudes and dispersion relations for hydrodynamic modes in an isotropic Fermi superfluid are derived. In this first paper we derive closed, decoupled, linearized kinetic equations for the bogolon spin density and total density in a Fermi superfluid with fluctuating superfluid velocity, and we discuss the form of the hydrodynamic equations that result from these equations.