  We derive the quantum Boltzmann equation (QBE) by using generalized
Landau-interaction parameters, obtained through the nonequilibrium Green's
function technique. This is a generalization of the usual QBE formalism to
non-Fermi liquid (NFL) systems, which do not have well-defined quasiparticles.
We apply this framework to a controlled low-energy effective field theory for
the Ising-nematic quantum critical point, in order to find the collective
excitations of the critical Fermi surface in the collisionless regime. We also
compute the nature of the dispersion after the addition of weak Coulomb
interactions. The zero angular momentum longitudinal vibrations of the Fermi
surface show a linear-in-wavenumber dispersion, which corresponds to the zero
sound of Landau's Fermi liquid theory. The Coulomb interaction modifies it to a
plasmon mode in the long-wavelength limit, which disperses as the square-root
of the wavenumber. Remarkably, our results show that the zero sound and plasmon
modes exhibit the same behaviour as in a Fermi liquid, although an NFL is
fundamentally different from the former.
