# Properties of the Boltzmann equation in the classical approximation

## Abstract

We examine the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since one has also access to the non-approximated result for comparison.

- Authors:

- Institut de Physique Theorique, Gif-sur-Yvette Cedex (France)
- RIKEN, Wako (Japan); Brookhaven National Lab., Upton, NY (United States)

- Publication Date:

- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1188218

- Report Number(s):
- BNL-107804-2015-JA

Journal ID: ISSN 1550-7998; PRVDAQ; KB0301020

- Grant/Contract Number:
- SC00112704

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review. D, Particles, Fields, Gravitation and Cosmology

- Additional Journal Information:
- Journal Volume: 90; Journal Issue: 12; Journal ID: ISSN 1550-7998

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

### Citation Formats

```
Epelbaum, Thomas, Gelis, François, Tanji, Naoto, and Wu, Bin.
```*Properties of the Boltzmann equation in the classical approximation*. United States: N. p., 2014.
Web. doi:10.1103/PhysRevD.90.125032.

```
Epelbaum, Thomas, Gelis, François, Tanji, Naoto, & Wu, Bin.
```*Properties of the Boltzmann equation in the classical approximation*. United States. doi:10.1103/PhysRevD.90.125032.

```
Epelbaum, Thomas, Gelis, François, Tanji, Naoto, and Wu, Bin. Tue .
"Properties of the Boltzmann equation in the classical approximation". United States.
doi:10.1103/PhysRevD.90.125032. https://www.osti.gov/servlets/purl/1188218.
```

```
@article{osti_1188218,
```

title = {Properties of the Boltzmann equation in the classical approximation},

author = {Epelbaum, Thomas and Gelis, François and Tanji, Naoto and Wu, Bin},

abstractNote = {We examine the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since one has also access to the non-approximated result for comparison.},

doi = {10.1103/PhysRevD.90.125032},

journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},

number = 12,

volume = 90,

place = {United States},

year = {Tue Dec 30 00:00:00 EST 2014},

month = {Tue Dec 30 00:00:00 EST 2014}

}

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