I have been reading about the various techniques that have been employed to study quantum field theories near equilibrium. It seems that the two main ways are the Schwinger-Keldysh (SK) and the Thermofield Dynamics (TFD) methods. It is clear that in equilibrium, both of these methods give the same answer (which also agrees with Matsubara's imaginary time method for dealing with equilibrium systems.) However, out of equilibrium, the generating functionals for SK and TFD appear different.
Question 1: Do SK and TFD actually give different results? Or is there some way to see that they are just two different representations of the same thing? I think the free-particle propagators in these two methods agree, but it's not clear to me that higher-order correlation functions for interacting theories will also agree.
Question 2: If SK and TFD are in fact different, which is the correct one to use? Is it some how possible that they are useful for calculating different kinds of observables of the same system?
