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 oneparticle 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 weakinteraction 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, B1348 LouvainlaNeuve (Belgium)
 Institut d'Astrophysique de Paris, CNRSUMR 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; BOLTZMANNVLASOV EQUATION; COLLISIONS; DEGREES OF FREEDOM; DISTRIBUTION; DISTRIBUTION FUNCTIONS; FERMIONS; PHOTONS; POLARIZATION; SPACETIME; SPIN; SPINORS; VELOCITY; WEAK INTERACTIONS
Citation Formats
Fidler, Christian, and Pitrou, Cyril, Email: christian.fidler@uclouvain.be, Email: pitrou@iap.fr. Kinetic theory of fermions in curved spacetime. United States: N. p., 2017.
Web. doi:10.1088/14757516/2017/06/013.
Fidler, Christian, & Pitrou, Cyril, Email: christian.fidler@uclouvain.be, Email: pitrou@iap.fr. Kinetic theory of fermions in curved spacetime. United States. doi:10.1088/14757516/2017/06/013.
Fidler, Christian, and Pitrou, Cyril, Email: christian.fidler@uclouvain.be, Email: pitrou@iap.fr. Thu .
"Kinetic theory of fermions in curved spacetime". United States.
doi:10.1088/14757516/2017/06/013.
@article{osti_22676172,
title = {Kinetic theory of fermions in curved spacetime},
author = {Fidler, Christian and Pitrou, Cyril, Email: christian.fidler@uclouvain.be, Email: 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 oneparticle 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 weakinteraction 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 = {10.1088/14757516/2017/06/013},
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}
}

We consider quantum fields in an external potential and show how, by using the Fourier transform on propagators, one can obtain the massshell constraint conditions and the LiouvilleVlasov equation for the Wigner distribution function. We then consider the Hadamard function G/sub 1/(x/sub 1/,x/sub 2/) of a real, free, scalar field in curved space. We postulate a form for the Fourier transform F/sup (//sup Q//sup )/(X,k) of the propagator with respect to the difference variable x = x/sub 1/x/sub 2/ on a Riemann normal coordinate centered at Q. We show that F/sup (//sup Q//sup )/ is the result of applying amore »

Improved effective potential in curved spacetime and quantum matterhigher derivative gravity theory
We develop a general formalism to study the renormalizationgroup (RG)improved effective potential for renormalizable gauge theories, including matter[ital R][sup 2]gravity, in curved spacetime. The result is given up to quadratic terms in curvature, and oneloop effective potentials may be easily obtained from it. As an example, we consider scalar QED, where dimensional transmutation in curved space and the phase structure of the potential (in particular, curvatureinduced phase transitions) are discussed. For scalar QED with higherderivative quantum gravity (QG), we examine the influence of QG on dimensional transmutation and calculate QG corrections to the scalartovector mass ratio. The phase structure ofmore » 
Finitetemperature quantum field theory in curved spacetime: Quasilocal effective Lagrangians
We use momentumspace techniques and a quasilocal expansion to derive the imaginarytime thermal Green's functions and the oneloop finitetemperature effective Lagrangians for lambdaphi/sup 4/ fields in curved spacetimes. These approximations are useful for treating quasiequilibrium conditions associated with gradual changes in the background fields and the background spacetimes. For problems in spacetimes with small curvature, we use a Riemann normal coordinate for the background metric, a derivative expansion for the background field, and a smallpropertime SchwingerDeWitt expansion to derive the finitetemperature effective Lagrangians. For problems in homogeneous cosmology we consider conformally related fields and the RobertsonWalker universe as background tomore » 
Functional measure for quantum field theory in curved spacetime
An examination of the functional measure for quantum field theory defined on a general curved background spacetime is presented. It is shown how to define the measure in field space to be invariant under general coordinate transformations based upon the simpler problem of defining an invariant inner product. The weight chosen for the variables of integration is seen not to matter in contrast with the claim of Fujikawa that they are uniquely specified. It is shown how the weight 1/2 variables advocated by Fujikawa are equivalent to working in a local orthonormal frame. In view of this, the interpretation ofmore »