Аннотация:
We develop Schwinger-Keldysh in-in formalism for generic nonequilibrium dynamical systems with mixed initial
states. We construct the generating functional of in-in Green's functions and expectation values for a generic
density matrix of the Gaussian type and show that the requirement of particle interpretation selects a
distinguished set of positive/negative frequency basis functions of the wave operator of the theory, which is
determined by the density matrix parameters. Then we consider a special case of the density matrix determined by
the Euclidean path integral of the theory, which in the cosmological context can be considered as a generalization
of the no-boundary pure state to the case of the microcanonical ensemble, and show that in view of a special
reflection symmetry its Wightman Green's functions satisfy Kubo-Martin-Schwinger periodicity conditions which
hold despite the nonequilibrium nature of the physical setup.