arXiv 1801.080972018-01hep-th

Bogoliubov变换与实时形式中的热算符表示

Bogoliubov transformation and the thermal operator representation in the real time formalism

Ashok Das, Atri Deshamukhya, Pushpa Kalauni, S. Panda

备注：: 9 pages, version to be published in Physical Review D
发表信息：: Phys. Rev. D 97, 045015 (2018)
DOI：: 10.1103/PhysRevD.97.045015

摘要：

早先\cite{brandt,brandt1}已经证明，在混合空间中，任何有限温度图和它的零温度对应物之间存在一种意想不到的简单关系，通过一个乘法标量算子（称为热算子），它承载了整个温度依赖性。这仅在虚时形式和实时形式的闭合时间路径（$σ=0$）（以及其共轭$σ=1$）中成立。我们研究的起源，这个运营商从更基本的Bogoliubov变换的行为，在动量空间，在实时形式主义\cite{takahashi,umezawa,pushpa}领域的加倍空间。我们展示了如何（$2\times 2$）Bogoliubov变换矩阵自然导致标量热运营商的$σ=0,1$，而它失败的任何其他值$0<σ<1$。这种分析还表明，广义标量热算子的描述，在混合空间中，甚至是可能的$0<σ<1$。我们还证明了动量空间中标量热算符关系的存在性。

英文摘要：

It has been shown earlier \cite{brandt,brandt1} that, in the mixed space, there is an unexpected simple relation between any finite temperature graph and its zero temperature counterpart through a multiplicative scalar operator (termed thermal operator) which carries the entire temperature dependence. This was shown to hold only in the imaginary time formalism and the closed time path ($σ=0$) of the real time formalism (as well as for its conjugate $σ=1$). We study the origin of this operator from the more fundamental Bogoliubov transformation which acts, in the momentum space, on the doubled space of fields in the real time formalisms \cite{takahashi,umezawa,pushpa}. We show how the ($2\times 2$) Bogoliubov transformation matrix naturally leads to the scalar thermal operator for $σ=0,1$ while it fails for any other value $0<σ<1$. This analysis also suggests that a generalized scalar thermal operator description, in the mixed space, is possible even for $0<σ<1$. We also show the existence of a scalar thermal operator relation in the momentum space.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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