  We study the spatially homogeneous phases of polar active particles in the
low density limit, and specifically the transition from the isotropic phase to
collective polar motion. We show that the fundamental quantity of interest for
the stability of the isotropic phase is the forward component of the momentum
change induced by binary scattering events. Building on the Boltzmann
formalism, we introduce an ansatz for the one-particle distribution and derive
a closed-form evolution equation for the order parameter. This approach yields
a very intuitive and physically meaningful criterion for the destabilization of
the isotropic phase, where the ansatz is exact. The criterion also predicts
whether the transition is continuous or discontinuous, as illustrated in three
different classes of models. The theoretical predictions are in excellent
agreement with numerical results.
