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Wick rotation to thermal of QFT in Minkowski space to thermal QFT, which is after this transformation analogue to statistical mechanics, does only describe equilibrium statistical mechanics. On page 227 of this paper it is said, that for dynamical questions beyond the equilibrium properties, the time coordinate has to be analytically continued to real Minkowski time.

This I do not understand at all. First of all, does analytic continuation not always generalize a real quantity to a complex quantity? This seems to go the other way round? Can somebody explain a bit why such an analytic continuation allows to describe the evolution of a system and how it works?

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Note entirely sure I get your question. Does my answer on questions/71645 help (the time contour bit, not the bit about renormalization)? –  Michael Brown Aug 14 '13 at 14:53
    
Hi @MichaelBrown thanks very much, very nice post and it answers my stupid question here too, will have to carefully reread it :-). –  Dilaton Aug 14 '13 at 22:24
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While I may certainly be missing the point, aren't the authors simply saying that if you start with an Euclidean theory, which describes a system at equilibrium, and want to analyze the actual dynamics, you need to analytically continue to the usual real Minkoski time (and then try to solve the problem)? Start from a system with “Euclidean time” wrapped around a torus with circumference T^-1, as they say, and unwrap it to "Minkoski time" to analyze a non-equilibrium dynamical problem.

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