# How to formally write down the Boltzmann equation?

Can someone write down the Boltzmann equation, not neglecting any of the variables of the involved functions and integrals? Specifically, how to concisely capture the "primed" variables in a sensible manner?

• It is equation 2.13 at homepage.univie.ac.at/franz.vesely/sp_english/sp/node7.html. The right hand side (collision term) depends on the type of collisions particles experinece. It is typically called collision operator since it is a function of distribution function. There are many possible operators. Each one of them describes certain phenomena – Gotaquestion Oct 19 '13 at 23:01
• @Gotaquestion: Well yeah, I ask for an explicit statement of it with all arguments written down in a line. Like an equation. Specifically, the primed velocities must be given computational meaning. Like (2.15), but without abbreviations - albeit $\sigma$ can stay as a not further unspecified function. – Nikolaj-K Oct 19 '13 at 23:21
• Have a look here [pma.caltech.edu/~mcc/Ph127/b/Lecture14.pdf ] where it is explained in more details. If you need more details have a look at the first 20 pages of E.M. Lifshitz book [amazon.com/… ] I don't think there is a need to write an answer if you are happy with details in those references, right? – Gotaquestion Oct 20 '13 at 17:40