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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 Carminati–McLenaghan invariants ： ウィキペディア英語版 Carminati–McLenaghan invariants In general relativity, the Carminati–McLenaghan invariants or CM scalars are a set of 16 scalar curvature invariants for the Riemann tensor. This set is usually supplemented with at least two additional invariants. ==Mathematical definition== The CM invariants consist of 6 real scalars plus 5 complex scalars, making a total of 16 invariants. They are defined in terms of the Weyl tensor $C\_$ and its right (or left) dual $^\; \backslash ,$ #$M\_1\; =\; \backslash frac\; \backslash ,\; S^\; \backslash ,\; S^\; \backslash ,\; \backslash left(\; C\_\; +\; i\; \backslash ,\; ^\backslash star\; C\}\_\; \backslash right)$ #$M\_2\; =\; \backslash frac\; \backslash ,\; S^\; \backslash ,\; S\_\; \backslash ,\; \backslash left(\; C\_\; \backslash ,\; C^\; -\; ^\backslash star\; C\}\_\; \backslash ,\; ^\backslash star\; C\}^\; \backslash right)\; +\; \backslash frac\; \backslash ,\; i\; \backslash ,\; S^\; \backslash ,\; S\_\; \backslash ,\; ^\backslash star\; C\}\_\; \backslash ,\; C^$ #$M\_5\; =\; \backslash frac\; \backslash ,\; S^\; \backslash ,\; S^\; \backslash ,\; \backslash left(\; C^\; +\; i\; \backslash ,\; ^\backslash star\; C\}^\; \backslash right)\; \backslash ,\; \backslash left(\; C\_\; \backslash ,\; C\_\; +\; ^\backslash star\; C\}\_\; \backslash ,\; ^\backslash star\; C\}\_\; \backslash right)$ The CM scalars have the following degrees: #$R$ is linear, #$R\_1,\; \backslash ,\; W\_1$ are quadratic, #$R\_2,\; \backslash ,\; W\_2,\; \backslash ,\; M\_1$ are cubic, #$R\_3,\; \backslash ,\; M\_2,\; \backslash ,\; M\_3$ are quartic, #$M\_4,\; \backslash ,\; M\_5$ are quintic. They can all be expressed directly in terms of the Ricci spinors and Weyl spinors, using Newman–Penrose formalism; see the link below. 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「Carminati–McLenaghan invariants」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.