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The nonequilibrium dynamics of quantum fields is an initial-value problem,which can be described by Kadanoff-Baym equations. Typically, and in particularwhen numerical solutions are demanded, these Kadanoff-Baym equations arerestricted to Gaussian initial states. However, physical initial states arenon-Gaussian correlated initial states. In particular, renormalizabilityrequires the initial state to feature n-point correlations that asymptoticallyagree with the vacuum correlations at short distances. In order to identifyphysical nonequilibrium initial states, it is therefore a precondition todescribe the vacuum correlations of the interacting theory within thenonequilibrium framework. In this paper, Kadanoff-Baym equations fornon-Gaussian correlated initial states describing vacuum and thermalequilibrium are derived from the 2PI effective action. A diagrammatic methodfor the explicit construction of vacuum and thermal initial correlations fromthe 2PI effective action is provided. We present numerical solutions ofKadanoff-Baym equations for a real scalar Phi^4 quantum field theory which takethe thermal initial 4-point correlation as the leading non-Gaussian correctioninto account. We find that this minimal non-Gaussian initial condition yieldsan approximation to the complete equilibrium initial state that isquantitatively and qualitatively significantly improved as compared to Gaussianinitial states.

Kadanoff-Baym Equations with Non-Gaussian Initial Conditions: The Equilibrium Limit