Kinetic theory of fermions in curved spacetime
  We build a statistical description of fermions, taking into account the spin
degree of freedom in addition to the momentum of particles, and we detail its
use in the context of the kinetic theory of gases of fermions particles. We
show that the one-particle distribution function needed to write a Liouville
equation is a spinor valued operator. The degrees of freedom of this function
are covariantly described by an intensity function and by a polarisation vector
which are parallel transported by free streaming. Collisions are described on
the microscopic level and lead to a Boltzmann equation for this operator. We
apply our formalism to the case of weak interactions, which at low energies can
be considered as a contact interaction between fermions, allowing us to discuss
the structure of the collision term for a few typical weak-interaction mediated
reactions. In particular we find for massive particles that a dipolar
distribution of velocities in the interacting species is necessary to generate
linear polarisation, as opposed to the case of photons for which linear
polarisation is generated from the quadrupolar distribution of velocities.
