Abstract
We study the evolution of the non-equilibrium quantum fields from a highly excited initial state in two approaches: the standard Keldysh–Schwinger diagram technique and the semiclassical expansion. We demonstrate explicitly that these two approaches coincide if the coupling constant g and the Plank constant hbar are simultaneously small. Also, we discuss loop diagrams of the perturbative approach, which are summed up by the leading order term of the semiclassical expansion. As an example, we consider shear viscosity for the scalar field theory at the leading semiclassical order. We introduce the new technique that unifies both semiclassical and diagrammatic approaches and open the possibility to perform the resummation of the semiclassical contributions.
Highlights
Nonequilibrium dense quantum fields define the initial stage of many physical problems
One of the most advanced approaches is the Keldysh– Schwinger diagram technique which provides a systematic way of studying nonequilibrium phenomena in quantum field theory [3,12,13,14]
This work aims to demonstrate that the Keldysh–Schwinger diagram technique and the classical statistical approach are two facets of one general way to deal with nonequilibrium quantum fields
Summary
Nonequilibrium dense quantum fields define the initial stage of many physical problems. This technique can be used for the systematic evaluation of thermodynamical and transport properties of the quantum systems at the thermal equilibrium [3,14] Another way to deal with the nonequilibrium initial state comes from a physical intuition and is based on the assumption that at high energies and/or high occupation numbers the dynamics of the quantum fields is semiclassical, so the classical equations of motion can be used [15,16,17,18,19,20,21,22,23,24,25]. This work aims to demonstrate that the Keldysh–Schwinger diagram technique and the classical statistical approach are two facets of one general way to deal with nonequilibrium quantum fields. It seems that these two approaches are quite different from a practical point of view.
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