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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 Wick contraction ： ウィキペディア英語版 Wick's theorem Wick's theorem is a method of reducing high-order derivatives to a combinatorics problem.〔Philips, 2001〕 It is named after Gian-Carlo Wick. It is used extensively in quantum field theory to reduce arbitrary products of creation and annihilation operators to sums of products of pairs of these operators. This allows for the use of Green's function methods, and consequently the use of Feynman diagrams in the field under study. A more general idea in probability theory is Isserlis’ theorem. ==Definition of contraction== For two operators $\backslash hat$ and $\backslash hat$ we define their contraction to be :$\backslash hat^\backslash bullet\backslash ,\; \backslash hat^\backslash bullet\; \backslash equiv\; \backslash hat\backslash ,\backslash hat\backslash ,\; -\; \backslash mathopen\; \backslash hat\backslash ,\backslash hat\; \backslash mathclose$ where $\backslash mathopen\; \backslash hat\; \backslash mathclose$ denotes the normal order of an operator $\backslash hat$. Alternatively, contractions can be denoted by a line joining $\backslash hat$ and $\backslash hat$. We shall look in detail at four special cases where $\backslash hat$ and $\backslash hat$ are equal to creation and annihilation operators. For $N$ particles we'll denote the creation operators by $\backslash hat\_i^\backslash dagger$ and the annihilation operators by $\backslash hat\_i$ ($i=1,2,3\backslash ldots,N$). They satisfy the usual commutation relations $()=\backslash delta\_$, where $\backslash delta\_$ denotes the Kronecker delta. We then have :$\backslash hat\_i^\backslash bullet\; \backslash ,\backslash hat\_j^\backslash bullet\; =\; \backslash hat\_i\; \backslash ,\backslash hat\_j\; \backslash ,-\; \backslash mathopen\backslash ,\backslash hat\_i\backslash ,\; \backslash hat\_j\backslash ,\backslash mathclose\backslash ,\; =\; 0$ :$\backslash hat\_i^\backslash ,\; \backslash hat\_j^\; =\; \backslash hat\_i^\backslash dagger\backslash ,\; \backslash hat\_j^\backslash dagger\; \backslash ,-\backslash ,\backslash mathopen\backslash hat\_i^\backslash dagger\backslash ,\backslash hat\_j^\backslash dagger\backslash ,\backslash mathclose\backslash ,\; =\; 0$ :$\backslash hat\_i^\backslash ,\; \backslash hat\_j^\backslash bullet\; =\; \backslash hat\_i^\backslash dagger\backslash ,\; \backslash hat\_j\; \backslash ,-\; \backslash mathopen\backslash ,\backslash hat\_i^\backslash dagger\; \backslash ,\backslash hat\_j\backslash ,\; \backslash mathclose\backslash ,=\; 0$ :$\backslash hat\_i^\backslash bullet\; \backslash ,\backslash hat\_j^=\; \backslash hat\_i\backslash ,\; \backslash hat\_j^\backslash dagger\; \backslash ,-\; \backslash mathopen\backslash ,\backslash hat\_i\backslash ,\backslash hat\_j^\backslash dagger\; \backslash ,\backslash mathclose\backslash ,\; =\; \backslash delta\_$ where $i,j\; =\; 1,\backslash ldots,N$. These relationships hold true for bosonic operators or fermionic operators because of the way normal ordering is defined. 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「Wick's 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.