Reanalysis of the hydrodynamic theory of fluid, polar-ordered flocks

I reanalyze the hydrodynamic theory of fluid, polar-ordered flocks. I find new linear terms in the hydrodynamic equations which slightly modify the anisotropy, but not the scaling, of the damping of sound modes. I also find that the nonlinearities allowed in equilibrium do not stabilize long-ranged order in spatial dimensions d=2, in accord with the Mermin-Wagner theorem. Nonequilibrium nonlinearities do stabilize long-ranged order in d=2, as argued by earlier work. Some of these were missed by earlier work; it is unclear whether or not they change the scaling exponents in d=2.