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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 Fermat’s and energy variation principles in field theory ： ウィキペディア英語版 Fermat’s and energy variation principles in field theory In general relativity the light is assumed to propagate in the vacuum along null geodesic in a pseudo-Riemannian manifold. Besides the geodesics principle in a classical field theory there exists the Fermat's principle for stationary gravity fields. Belayev has proposed variational method without the violation of isotropy of the path of the lightlike particle, giving equations identical to those that follow from Fermat's principle. In this method the action principle leads to condition of zero variational derivative of the integral of energy, and it is applied also to non-stationary gravity fields. == Fermat's principle == In more general case for conformally stationary spacetime with coordinates $(t,x^1,x^2,x^3)$ a Fermat metric takes form , where conformal factor $f(t,x)$ depending on time $t$ and space coordinates $x^$ does not affect the lightlike geodesics apart from their parametrization. Fermat's principle for a pseudo-Riemannian manifold states that the light ray path between points $x\_a=(x^1\_a,x^2\_a,x^3\_a)$ and $x\_b=(x^1\_b,x^2\_b,x^3\_b)$ corresponds to zero variation of action $S=\backslash int^\_\backslash left(\backslash sqrt\; \backslash frac\; \backslash frac\}+\backslash phi\_(x)\backslash frac\; \backslash right)d\backslash mu$, where $\backslash mu$ is any parameter ranging over an interval $(\backslash mu\_b)$ and varying along curve with fixed endpoints $x\_a=x(\backslash mu\_a)$ and $x\_b=x(\backslash mu\_b)$. 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「Fermat’s and energy variation principles in field theory」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.