# Kinetic theory of fermions in curved spacetime

## 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.

- Authors:

- Catholic University of Louvain, Center for Cosmology, Particle Physics and Phenomenology (CP3), 2, Chemin du Cyclotron, B-1348 Louvain-la-Neuve (Belgium)
- Institut d'Astrophysique de Paris, CNRS-UMR 7095, UPMC—Paris VI, Sorbonne Universités, 98 bis Bd Arago, 75014 Paris (France)

- Publication Date:

- OSTI Identifier:
- 22676172

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 06; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOLTZMANN EQUATION; BOLTZMANN-VLASOV EQUATION; COLLISIONS; DEGREES OF FREEDOM; DISTRIBUTION; DISTRIBUTION FUNCTIONS; FERMIONS; PHOTONS; POLARIZATION; SPACE-TIME; SPIN; SPINORS; VELOCITY; WEAK INTERACTIONS

### Citation Formats

```
Fidler, Christian, and Pitrou, Cyril, E-mail: christian.fidler@uclouvain.be, E-mail: pitrou@iap.fr.
```*Kinetic theory of fermions in curved spacetime*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/06/013.

```
Fidler, Christian, & Pitrou, Cyril, E-mail: christian.fidler@uclouvain.be, E-mail: pitrou@iap.fr.
```*Kinetic theory of fermions in curved spacetime*. United States. doi:10.1088/1475-7516/2017/06/013.

```
Fidler, Christian, and Pitrou, Cyril, E-mail: christian.fidler@uclouvain.be, E-mail: pitrou@iap.fr. Thu .
"Kinetic theory of fermions in curved spacetime". United States.
doi:10.1088/1475-7516/2017/06/013.
```

```
@article{osti_22676172,
```

title = {Kinetic theory of fermions in curved spacetime},

author = {Fidler, Christian and Pitrou, Cyril, E-mail: christian.fidler@uclouvain.be, E-mail: pitrou@iap.fr},

abstractNote = {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.},

doi = {10.1088/1475-7516/2017/06/013},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 06,

volume = 2017,

place = {United States},

year = {Thu Jun 01 00:00:00 EDT 2017},

month = {Thu Jun 01 00:00:00 EDT 2017}

}