Mean free path in QFT I'm trying to understand the hydrodynamic approximation of a general QFT when the large $k$ and $\omega$ DOF have been integrated out i.e that at highly enough temperature every non-trivial QFT equilibrates into a fluid phase.
We know that in the hydrodynamics we have $\lambda \gg l_{\text{mfp}} $. But I don't really get some things in order to completely make the transition to the QFT picture:


*

*What is the $l_{\text{mfp}}$ in a QFT?

*How we put/descirbe temperature on a QFT?
 A: The standard way to put in a temperature is to go to imaginary time (euclidean space) and impose periodic/anti-periodic boundary conditions on bosonic/fermionic fields
$$
\phi(x,\tau)=\phi(x,\tau+\beta) , \;\;\;\;
\psi(x,\tau)=-\psi(x,\tau+\beta),
$$
where $\beta=1/T$. This ensures that the path integral represents the partition function $Z=Tr[\exp(-\beta H)]$. 
Hydrodynamics is a low-energy, long wavelength approximation for the correlation functions of the theory. In the weak coupling limit (or in strong coupling, provided weakly coupled quasi-particles emerge), the hydrodynamic expansion is valid for $kl_{mfp}<1$ and $\omega\tau_{mft}<1$, where $l_{mfp}=1/(n\sigma)$. Here, the density $n$ and mean cross section can be computed in ordinary perturbation theory. 
In strong coupling no simple criterion is available. There may be no quasi-particles, and as a result no quasi-particle cross-section to compute. You can still ask, however, what the regime of validity of hydrodynamics is. There will be some breakdown scale $\Lambda$ such that hydro works for $\omega<\Lambda$. In strongly coupled quasi-conformal theories (a la Ads/CFT) we find $\Lambda\sim T$. 
