Abstract
We discuss the thermalization process in kinetic approximation in the presence of non-zero initial anomalous quantum expectation values on top of an initial non-Planckian (non-thermal) level population. In particular, we derive a system of “kinetic” equations for the level population and anomalous expectation values in four-dimensional massive scalar field theory with φ4 self-interaction. We analytically show, in the linear approximation, that for their small initial values, the anomalous quantum averages relax down to zero. Furthermore, we show analytically that this system does not have an equilibrium solution with non-zero time independent anomalous expectation value.
Highlights
The understanding of quantum field theory dynamics over strong field backgrounds demands the consideration of correlation functions over quantum states with non-zero anomalous quantum expectation values or anomalous averages
Our goal is to show that such a state will evolve in time towards the Planckian level population, np = eβ p1−1, and zero anomalous average
We have considered the approach to such an equilibrium state in which the anomalous average is zero
Summary
The understanding of quantum field theory dynamics over strong field backgrounds demands the consideration of correlation functions over quantum states with non-zero anomalous quantum expectation values or anomalous averages. In a quantum field theory over strong background fields, even for zero initial values, the anomalous averages are generated dynamically in loop corrections [3]. The consideration of states with non-zero anomalous averages in flat space quantum field theory can be a suitable playground for the development of methods to work in similar situations over strong background fields. We consider an initial state containing a non-Planckian (non-thermal) level population, which is expressed via Tr[∧ρa+q aq ] ≡ a+q aq , and anomalous averages, Tr[ρaqaq ] ≡ aqaq. The final state of the thermalization process is described by the Planckian distribution of modes, np, over the Poincare invariant ground state To show this phenomenon, we derive a system of kinetic equations for the level population and anomalous averages. We derive the system of kinetic equations for np and χp without the latter assumptions
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