Introductory text to the Boltzmann equation?

Question

I'm searching for a good introductory text to the Boltzmann equation and how it gets applied in the relativistic case as well?

Answer 1

There are many introductions to kinetic theory and the Boltzmann equation. I tend to think that you can't go wrong with volume X of Landau and Lifshitz, but Landau is very brief on the relativistic case.

A nice general introduction that covers the relativistic (and, to some extent, the quantum) case is Richard Liboff, Kinetic Theory.

There are specialized books on the relativistic theory too. An old one is John Stewart, Non-Equilibrium Relativistic Kinetic Theory (mostly about the basics), or De Groot et al., Relativistic Kinetic Theory (includes applications to mixtures of various elementary particles). Cercignani and Kremer, The Relativistic Boltzmann Equation: Theory and Applications also covers the general relativistic case. A more recent book is Vereshchagin and Aksenov, Relativistic Kinetic Theory, which has some applications to astrophysical plasmas.

Many books describe applications of relativistic kinetic theory to problems in cosmology, astrophysical fluid dynamics, and relativistic heavy ion collisions, for example Weinberg's book on cosmology, or Rezolla's book on relativistic fluid dynamics.