论文标题
一般状态中的Wightman相关器的图表学：简单的谐波和无声振荡器的情况
Diagrammatics for Wightman Correlators in General States: The Cases of the Simple Harmonic and Anharmonic Oscillators
论文作者
论文摘要
简单谐波振荡器的位置运算符的计算真空期望值的机制已经确定。它基于一个wick定理，它使一个人可以根据\ emph {pairwise收缩}的产物分解如此数量，这是一次性位置运算符的真空期望值一次，一次是摄取的两个。该结果自然会导致一种计算此类相关因子的图形方法，并且已经以Feynman图的形式众所周知。我们将此设置概括为包含简单谐波振荡器的一般密度矩阵中的一般排序算子（Wightman序列）的期望值。最初是针对这种情况开发的Wick定理，因此制定了图表。还分析了\ emph {anharmonic}振荡器的一般密度矩阵中的Wightman相关器，并为他们开发了图形形式主义。
The machinery of computing vacuum expectation values of a time-ordered sequence of position operators of the simple harmonic oscillator is already well established. It rests on a Wick theorem, which enables one to decompose such a quantity in terms of products of \emph{pairwise contractions}, which are vacuum expectation values of a time-ordered sequence of position operators taken two at a time. This result naturally leads to a diagrammatic approach of computing such correlators, and is already well known in the form of Feynman diagrams. We generalise this setup to encompass expectation values of a general ordered sequence of position operators (Wightman sequences) in general density matrices of the simple harmonic oscillator. A Wick theorem is first developed for this situation and consequently a diagrammatics is laid down. Wightman correlators in general density matrices of the \emph{anharmonic} oscillator are also analysed and a diagrammatic formalism is developed for them too.
