Nonequilibrium Schwinger-Keldysh formalism for density matrix states: analytic properties and implications in cosmology

• URL: http://arxiv.org/abs/2309.03687v1
• Date: Thu, 7 Sep 2023 13:01:55 GMT
• Title: Nonequilibrium Schwinger-Keldysh formalism for density matrix states: analytic properties and implications in cosmology
• Authors: Andrei O. Barvinsky, Nikita Kolganov
• Abstract summary: We develop Schwinger-Keldysh in-in formalism for generic nonequilibrium dynamical systems. In view of a special reflection symmetry our Wightman Green's functions satisfy Kubo-Martin-Schwinger periodicity conditions. Rich analyticity structure in the complex plane of the time variable reveals the combined Euclidean-Lorentzian evolution of the theory.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Motivated by cosmological Hartle-Hawking and microcanonical density matrix prescriptions for the quantum state of the Universe we develop Schwinger-Keldysh in-in formalism for generic nonequilibrium dynamical systems with the initial density matrix. We build 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. Rich analyticity structure in the complex plane of the time variable reveals the combined Euclidean-Lorentzian evolution of the theory, which depending on the properties of the initial density matrix can be interpreted as a decay of a classically forbidden quantum state.

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