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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 Synge's world function ： ウィキペディア英語版 Synge's world function In general relativity, Synge's world function is an example of a bitensor, i.e. a tensorial function of pairs of points in the spacetime. Let $x,\; x\text{'}$ be two points in spacetime, and suppose $x$ belongs to a normal convex neighborhood of $x$ so that there exists a unique geodesic $\backslash gamma(\backslash lambda)$ from $x$ to $x\text{'}$, up to the affine parameter $\backslash lambda$. Suppose $\backslash gamma(\backslash lambda\_0)\; =\; x\text{'}$ and $\backslash gamma(\backslash lambda\_1)\; =\; x$. Then Synge's world function is defined as: :$\backslash sigma(x,x\text{'})\; =\; \backslash frac\; (\backslash lambda\_-\backslash lambda\_)\; \backslash int\_\}\; g\_(z)\; t^t^\; d\backslash lambda$ where the integral is evaluated along the geodesic connecting the two points. That is, $\backslash sigma(x,x\text{'})$ is half the square of the geodesic length from $x$ to $x\text{'}$. Synge's world function is well-defined, since the integral above is invariant under reparametrization. In particular, for Minkowski spacetime, the Synge's world function simplifies to half the spacetime interval between the two points: :$\backslash sigma(x,x\text{'})\; =\; \backslash frac\; \backslash eta\_\; (x-x\text{'})^\; (x-x\text{'})^$ == References == http://relativity.livingreviews.org/Articles/lrr-2011-7/fulltext.html 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「Synge's world function」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.