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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 Four-gradient ： ウィキペディア英語版 Four-gradient In differential geometry, the four-gradient is the four-vector analogue of the gradient from Gibbs-Heaviside vector calculus. ==Definition== The covariant components compactly written in index notation are:〔The Cambridge Handbook of Physics Formulas, G. Woan, Cambridge University Press, 2010, ISBN 978-0-521-57507-2〕 :$\backslash dfrac\; =\; \backslash left(\backslash frac\backslash frac,\; \backslash vec\backslash right)\; =\; \backslash left(\backslash frac,\; \backslash vec\backslash right)\; =\; \backslash partial\_\backslash alpha\; =\; \_$ implies the ''partial differentiation'' with respect to $x^\backslash alpha$. This is not the same as a semi-colon, used for the covariant derivative. The contravariant components are:〔The Cambridge Handbook of Physics Formulas, G. Woan, Cambridge University Press, 2010, ISBN 978-0-521-57507-2〕 :$\backslash mathbf\; =\; \backslash partial^\backslash alpha\; \backslash \; =\; g^\; \backslash partial\_\backslash beta\; =\; \backslash left(\backslash frac\; \backslash frac,\; -\backslash vec\; \backslash right)=\; \backslash left(\backslash frac,\; -\backslash vec\backslash right)\; =\; \backslash left(\backslash frac,\; -\backslash partial\_x,-\backslash partial\_y,-\backslash partial\_z\backslash right)$ where ''gαβ'' is the metric tensor, which here has been chosen for flat spacetime with the metric signature (+,−,−,−). Alternative symbols to $\backslash partial\_\backslash alpha$ are $\backslash Box$ and ''D''. 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「Four-gradient」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.