The Boltzmann equation in classical Yang–Mills theory

V. Mathieu; A. H. Mueller; D. N. Triantafyllopoulos

doi:10.1140/epjc/s10052-014-2873-8

EPJ

The Boltzmann equation in classical Yang–Mills theory

V. Mathieu¹^,2, A. H. Mueller³ and D. N. Triantafyllopoulos⁴^*

¹ Department of Physics, Indiana University, Bloomington, IN, 47405, USA
² Center for Exploration of Energy and Matter, Indiana University, Bloomington, IN, 47403, USA
³ Department of Physics, Columbia University, New York, NY, 10027, USA
⁴ European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*) and Fondazione Bruno Kessler, Strada delle Tabarelle 286, 38123 , Villazzano (TN), Italy

Received: 18 March 2014
Accepted: 22 April 2014
Published online: 9 May 2014

Abstract

We give a detailed derivation of the Boltzmann equation, and in particular its collision integral, in classical field theory. We first carry this out in a scalar theory with both cubic and quartic interactions and subsequently in a Yang–Mills theory. Our method does not rely on a doubling of the fields, rather it is based on a diagrammatic approach representing the classical solution to the problem.