# Kinetic theory of fermions in curved spacetime

## TL;DR

This paper develops a covariant kinetic theory for fermions in curved spacetime, incorporating spin and polarization, and derives a Boltzmann equation including weak interaction effects.

## Contribution

It introduces a spinor-valued distribution function and a covariant formalism for fermion polarization and collisions in curved spacetime.

## Key findings

- Polarization arises from dipolar velocity distributions in massive fermions.
- The formalism applies to weak interactions, providing a detailed collision term.
- Linear polarization requires specific velocity distributions, differing from photons.

## Abstract

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.