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arXiv 2003.06395hep-phcond-mat.stat-mechhep-thnucl-th
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半经典近似与Keldysh-Schwinger图解技术的结合：标量$φ^4$

Semiclassical Approximation meets Keldysh-Schwinger diagrammatic technique: Scalar $φ^4$

A. A. Radovskaya, A. G. Semenov

备注：
10 pages, many diagrams
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摘要：

我们用两种方法研究了高激发初态非平衡量子场的演化：标准Keldysh-Schwinger图方法和半经典展开方法。我们明确地表明，这两种方法相吻合，如果耦合常数$g$和普朗克常数$\hbar$是小的同时。此外，我们讨论了微扰方法的回路图，这些回路图由半经典展开式的首阶项概括。作为一个例子，我们考虑在领先的半经典阶的标量场理论的剪切粘性。我们介绍的新技术，统一了半经典和图解的方法，并打开的可能性，执行remation的半经典的贡献。

英文摘要：

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 small simultaneously. 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.

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