  We review the effective field theory associated with the superfluid phonons
that we use for the study of transport properties in the core of superfluid
neutrons stars in their low temperature regime. We then discuss the shear and
bulk viscosities together with the thermal conductivity coming from the
collisions of superfluid phonons in neutron stars. With regard to shear, bulk,
and thermal transport coefficients, the phonon collisional processes are
obtained in terms of the equation of state and the superfluid gap. We compare
the shear coefficient due to the interaction among superfluid phonons with
other dominant processes in neutron stars, such as electron collisions. We also
analyze the possible consequences for the r-mode instability in neutron stars.
As for the bulk viscosities, we determine that phonon collisions contribute
decisively to the bulk viscosities inside neutron stars. For the thermal
conductivity resulting from phonon collisions, we find that it is temperature
independent well below the transition temperature. We also obtain that the
thermal conductivity due to superfluid phonons dominates over the one resulting
from electron-muon interactions once phonons are in the hydrodynamic regime. As
the phonons couple to the $Z$ electroweak gauge boson, we estimate the
associated neutrino emissivity. We also briefly comment on how the superfluid
phonon interactions are modified in the presence of a gravitational field or in
a moving background.
