# What is the proper time used in relativistic non-equilibrium statistical physics?

In the literature one often finds covariant relativistic generalizations of classical non equilibrium statistical equations (Boltzmann, Vlasov, Landau, Fokker-Planck, etc...) but I wonder what is the meaning of the time which is used. As far as I know, one can only write the interaction between two relativistic charged particles by doing the computation in the proper space-time frame of one of the particles. With three relativistic charged particles I am already wondering about how to tackle the problem of proper time, so for N close to a mole...I am lost. Since non-equilibrium statistical mechanics is derived from Hamiltonian mechanics, I can reformulate my question as follows. What is the Hamiltonian of N relativistic interacting charged particles ?

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icmp.lviv.ua/journal/zbirnyk.25/001/art01.pdf "Classical relativistic system of N charges. Hamiltonian description, forms of dynamics, and partition function" looks as if it answers exactly your question. –  John Rennie Jul 18 '12 at 12:08
Exactly what I was looking for. Thank's a lot –  Shaktyai Jul 18 '12 at 13:32
@JohnRennie perhaps you could post that as an answer? (with a brief statement of what the article actually says that answers the question) –  David Z Jul 19 '12 at 6:40
@DavidZaslavsky a quick glance at the article convinced me that a brief description would be hard! The fact I found it is more a testament to my Google skills than my deep knowledge of relativistic statistical thermodynamics :-) –  John Rennie Jul 19 '12 at 6:55
The paper is quite complex, so far my researches to solve the problem has only brought back this paper: cft.edu.pl/~laturski/Physica/… I am not sure I understand how they have avoided the retarded time for each particle ... –  Shaktyai Jul 20 '12 at 11:18