  We study the dynamic response of a Fermi liquid in the spin, charge and
nematic channels beyond the random phase approximation for the dynamically
screened Coulomb potential. In all the channels, one-loop order corrections to
the irreducible susceptibility result in a non-zero spectral weight of the
corresponding fluctuations above the particle-hole continuum boundary. It is
shown that the imaginary part of the spin susceptibility,
$\text{Im}\chi_{s}(\bf{q},\omega)$, falls off as $q^2/\omega$ for frequencies
above the continuum boundary ($\omega\gg v_{F} q$) and below the
model-dependent cutoff frequency, whereas the imaginary part of the charge
susceptibility, $\text{Im}\chi_c(\bf{q},\omega)$, falls off as $(q/k_F)^2
q^2/\omega$ for frequencies above the plasma frequency. An extra factor of
$(q/k_F)^2$ in $\text{Im}\chi_c(\bf{q},\omega)$ as compared to
$\text{Im}\chi_{s}(\bf{q},\omega)$ is a direct consequence of Galilean
invariance. The imaginary part of the nematic susceptibility increases linearly
with $\omega$ up to a peak at the ultraviolet energy scale-- the plasma
frequency and/or Fermi energy--and then decreases with $\omega$. We also obtain
explicit forms of the spin susceptibility from the kinetic equation in the
collisionless limit and for the Landau function that contains up to first three
harmonics.
