翻訳と辞書 Words near each other ・ "O" Is for Outlaw ・ "O"-Jung.Ban.Hap. ・ "Ode-to-Napoleon" hexachord ・ "Oh Yeah!" Live ・ "Our Contemporary" regional art exhibition (Leningrad, 1975) ・ "P" Is for Peril ・ "Pimpernel" Smith ・ "Polish death camp" controversy ・ "Pro knigi" ("About books") ・ "Prosopa" Greek Television Awards ・ "Pussy Cats" Starring the Walkmen ・ "Q" Is for Quarry ・ "R" Is for Ricochet ・ "R" The King (2016 film) ・ "Rags" Ragland ・ ! (album) ・ ! (disambiguation) ・ !! ・ !!! ・ !!! (album) ・ !!Destroy-Oh-Boy!! ・ !Action Pact! ・ !Arriba! La Pachanga ・ !Hero ・ !Hero (album) ・ !Kung language ・ !Oka Tokat ・ !PAUS3 ・ !T.O.O.H.! ・ !Women Art Revolution Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Stewart–Walker ： ウィキペディア英語版 Stewart–Walker lemma The Stewart–Walker lemma provides necessary and sufficient conditions for the linear perturbation of a tensor field to be gauge-invariant. $\backslash Delta\; \backslash delta\; T\; =\; 0$ if and only if one of the following holds 1. $T\_\; =\; 0$ 2. $T\_$ is a constant scalar field 3. $T\_$ is a linear combination of products of delta functions $\backslash delta\_^$ == Derivation == A 1-parameter family of manifolds denoted by $\backslash mathcal\_$ with $\backslash mathcal\_\; =\; \backslash mathcal^$ has metric $g\_\; =\; \backslash eta\_\; +\; \backslash epsilon\; h\_$. These manifolds can be put together to form a 5-manifold $\backslash mathcal$. A smooth curve $\backslash gamma$ can be constructed through $\backslash mathcal$ with tangent 5-vector $X$, transverse to $\backslash mathcal\_$. If $X$ is defined so that if $h\_$ is the family of 1-parameter maps which map $\backslash mathcal\; \backslash to\; \backslash mathcal$ and $p\_\; \backslash in\; \backslash mathcal\_$ then a point $p\_\; \backslash in\; \backslash mathcal\_$ can be written as $h\_(p\_)$. This also defines a pull back $h\_^$ that maps a tensor field $T\_\; \backslash in\; \backslash mathcal\_$ back onto $\backslash mathcal\_$. Given sufficient smoothness a Taylor expansion can be defined :$h\_^(T\_)\; =\; T\_\; +\; \backslash epsilon\; \backslash ,\; h\_^(\backslash mathcal\_T\_)\; +\; O(\backslash epsilon^)$ $\backslash delta\; T\; =\; \backslash epsilon\; h\_^(\backslash mathcal\_T\_)\; \backslash equiv\; \backslash epsilon\; (\backslash mathcal\_T\_)\_$ is the linear perturbation of $T$. However, since the choice of $X$ is dependent on the choice of gauge another gauge can be taken. Therefore the differences in gauge become $\backslash Delta\; \backslash delta\; T\; =\; \backslash epsilon(\backslash mathcal\_T\_)\_0\; -\; \backslash epsilon(\backslash mathcal\_T\_)\_0\; =\; \backslash epsilon(\backslash mathcal\_T\_\backslash epsilon)\_0$. Picking a chart where $X^\; =\; (\backslash xi^\backslash mu,1)$ and $Y^a\; =\; (0,1)$ then $X^-Y^\; =\; (\backslash xi^,0)$ which is a well defined vector in any $\backslash mathcal\_\backslash epsilon$ and gives the result :$\backslash Delta\; \backslash delta\; T\; =\; \backslash epsilon\; \backslash mathcal\_T\_0.\backslash ,$ The only three possible ways this can be satisfied are those of the lemma. 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「Stewart–Walker lemma」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.