翻訳と辞書 Words near each other ・ Stewartstown, West Virginia ・ Stewartsville (disambiguation) ・ Stewartsville, Indiana ・ Stewartsville, Missouri ・ Stewartsville, New Jersey ・ Stewartville ・ Stewartville Formation ・ Stewartville, Alabama ・ Stewartville, California ・ Stewartville, Coosa County, Alabama ・ Stewartville, Guyana ・ Stewartville, Lauderdale County, Alabama ・ Stewartville, Minnesota ・ Stewart–Tolman effect ・ Stewart–Treves syndrome ・ Stewart–Walker lemma ・ Stewiacke ・ Stewiacke railway station ・ Stewiacke River ・ Stewiacke Valley ・ Stewie ・ Stewie (cat) ・ Stewie Dempster ・ Stewie Goes for a Drive ・ Stewie Griffin ・ Stewie is Enceinte ・ Stewie Kills Lois and Lois Kills Stewie ・ Stewie Loves Lois ・ Stewie Speer ・ Stewie, Chris, & Brian's Excellent Adventure 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 lemma ： 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.