Abstract
We discuss the renormalization of the initial value problem in Nonequilibrium Quantum Field Theory within a simple, yet instructive, example and show how to obtain a renormalized time evolution for the two-point functions of a scalar field and its conjugate momentum at all times. The scheme we propose is applicable to systems that are initially far from equilibrium and compatible with non-secular approximation schemes which capture thermalization. It is based on Kadanoff-Baym equations for non-Gaussian initial states, complemented by usual vacuum counterterms. We explicitly demonstrate how various cutoff-dependent effects peculiar to nonequilibrium systems, including time-dependent divergences or initial-time singularities, are avoided by taking an initial non-Gaussian three-point vacuum correlation into account.
Highlights
Quantum field theory out of equilibrium has received a lot of attention in recent years, especially within the framework of the Kadanoff-Baym equations [1]
Many interesting approaches have been devoted to understanding and tackling the problem, from studies in the Hartree approximation or in perturbation theory [6,7,8,9,10] which do not capture thermalization or are not free of secular terms, to approaches based on appropriately chosen external sources [11,12] or on the use of information about the time evolution prior to the initialization time [13] which depart in spirit from the strict initial value problem, and restrict the control over the initial state
We present a consistent formulation dealing with both secular terms and UV divergences, in which the only ingredient is a proper description of the initial state
Summary
Quantum field theory out of equilibrium has received a lot of attention in recent years, especially within the framework of the Kadanoff-Baym equations [1]. It is important to stress that, when it comes to discussing the renormalization out-of-equilibrium, few analytical results are known, especially in any framework that deals simultaneously with the secularity problem (and goes beyond perturbation theory). For this reason, in this work we focus on a specific model/approximation that allows us to exhibit the features which render. V, we discuss yet another peculiar feature of the Gaussian initial state and how it is cured by the three-point initial correlations
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