  We extend the kinetic operator formalism developed in the companion paper
[H.Guo,arXiv:2311.03455] to study the general eigenvalues of the fluctuation
normal modes. We apply the formalism to calculate the optical conductivity of a
critical Fermi surface near the Ising-Nematic quantum critical point. We find
that the conductivity is the sum of multiple conduction channels including both
the soft and non-soft eigenvectors of the kinetic operator, and therefore it is
not appropriate to interpret the optical conductivity using extended Drude
formula for momentum conserved systems. We also show that the propagation of
the FS soft modes is governed by a Boltzmann equation from which hydrodynamics
emerges. We calculate the viscosity and it shows clear signature of the
non-Fermi liquid physics.
