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

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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 ?


This post imported from StackExchange Physics at 2016-10-30 15:19 (UTC), posted by SE-user Shaktyai

asked Jul 18, 2012 in Theoretical Physics by Shaktyai (40 points) [ revision history ]
edited Oct 30, 2016 by Dilaton
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.

This post imported from StackExchange Physics at 2016-10-30 15:19 (UTC), posted by SE-user John Rennie
Exactly what I was looking for. Thank's a lot

This post imported from StackExchange Physics at 2016-10-30 15:19 (UTC), posted by SE-user Shaktyai
@JohnRennie perhaps you could post that as an answer? (with a brief statement of what the article actually says that answers the question)

This post imported from StackExchange Physics at 2016-10-30 15:19 (UTC), posted by SE-user David Z
@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 :-)

This post imported from StackExchange Physics at 2016-10-30 15:19 (UTC), posted by SE-user John Rennie
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 ...

This post imported from StackExchange Physics at 2016-10-30 15:19 (UTC), posted by SE-user Shaktyai

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