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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 Feynman slash notation ： ウィキペディア英語版 Feynman slash notation In the study of Dirac fields in quantum field theory, Richard Feynman invented the convenient Feynman slash notation (less commonly known as the Dirac slash notation). If ''A'' is a covariant vector (i.e., a 1-form), :$A\backslash !\backslash !\backslash !/\backslash \; \backslash stackrel\backslash \; \backslash gamma^\backslash mu\; A\_\backslash mu$ using the Einstein summation notation where ''γ'' are the gamma matrices. ==Identities== Using the anticommutators of the gamma matrices, one can show that for any $a\_\backslash mu$ and $b\_\backslash mu$, :$a\backslash !\backslash !\backslash !/a\backslash !\backslash !\backslash !/=a^\backslash mu\; a\_\backslash mu=a^2$ :$a\backslash !\backslash !\backslash !/b\backslash !\backslash !\backslash !/+b\backslash !\backslash !\backslash !/a\backslash !\backslash !\backslash !/\; =\; 2\; a\; \backslash cdot\; b\; \backslash ,$. In particular, :$\backslash partial\backslash !\backslash !\backslash !/^2=\backslash partial^2.$ Further identities can be read off directly from the gamma matrix identities by replacing the metric tensor with inner products. For example, ::$\backslash operatorname(a\backslash !\backslash !\backslash !/b\backslash !\backslash !\backslash !/)\; =\; 4\; a\; \backslash cdot\; b$ ::$\backslash operatorname(a\backslash !\backslash !\backslash !/b\backslash !\backslash !\backslash !/c\backslash !\backslash !\backslash !/d\backslash !\backslash !\backslash !/)\; =\; 4\; \backslash left(b)(c\; \backslash cdot\; d)\; -\; (a\; \backslash cdot\; c)(b\; \backslash cdot\; d)\; +\; (a\; \backslash cdot\; d)(b\; \backslash cdot\; c)\; \backslash right)$ ::$\backslash operatorname(\backslash gamma\_5\; a\backslash !\backslash !\backslash !/b\backslash !\backslash !\backslash !/c\backslash !\backslash !\backslash !/d\backslash !\backslash !\backslash !/)\; =\; 4\; i\; \backslash epsilon\_\; a^\backslash mu\; b^\backslash nu\; c^\backslash lambda\; d^\backslash sigma$ ::$\backslash gamma\_\backslash mu\; a\backslash !\backslash !\backslash !/\; \backslash gamma^\backslash mu\; =\; -2\; a\backslash !\backslash !\backslash !/$. ::$\backslash gamma\_\backslash mu\; a\backslash !\backslash !\backslash !/\; b\backslash !\backslash !\backslash !/\; \backslash gamma^\backslash mu\; =\; 4\; a\; \backslash cdot\; b\; \backslash ,$ ::$\backslash gamma\_\backslash mu\; a\backslash !\backslash !\backslash !/\; b\backslash !\backslash !\backslash !/\; c\backslash !\backslash !\backslash !/\; \backslash gamma^\backslash mu\; =\; -2\; c\backslash !\backslash !\backslash !/\; b\backslash !\backslash !\backslash !/\; a\backslash !\backslash !\backslash !/\; \backslash ,$ :where ::$\backslash epsilon\_\; \backslash ,$ is the Levi-Civita symbol. 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「Feynman slash notation」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.