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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク cluster decomposition theorem ： ウィキペディア英語版 cluster decomposition theorem In physics, the cluster decomposition property is related to locality in quantum field theory. In a quantum field theory having this property, the vacuum expectation value of a product of many operators - each of them being either in region A or in region B where A and B are very separated - asymptotically equals the product of the expectation value of the product of the operators in A, times a similar factor from the region B. Consequently, sufficiently separated regions behave independently. If A1, ..., An are n operators each localized in a bounded region and $U(a)$ represents the unitary operator actively translating the Hilbert space by the vector a, then if we pick some subset of the n operators to translate, :$\backslash lim\_\backslash langle\backslash Omega|A\text{'}\_1\backslash cdots\; A\text{'}\_n|\backslash Omega\backslash rangle-\backslash langle\backslash Omega|\backslash prod\_\}U(a)A\_i\; U^(a)|\backslash Omega\backslash rangle=0$ where $\backslash vert\; \backslash Omega\; \backslash rangle$ is the vacuum state, and : provided a is a spacelike vector. Expressed in terms of the connected correlation functions, it means if some of the arguments of the connected correlation function are shifted by large spacelike separations, the function goes to zero. This property only holds if the vacuum is a pure state. If the vacuum is degenerate and we have a mixed state, the cluster decomposition property fails. If the theory has a mass gap $m>0$, then there is a value a0 beyond which the connected correlation function is absolutely bounded by $C\; e^$ where $C$ is some coefficient and $\backslash vert\; a\; \backslash vert$ is the length of the vector $a$ for $\backslash vert\; a\; \backslash vert\; >\; a\_0$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「cluster decomposition theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.