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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 Gell-Mann matrices ： ウィキペディア英語版 Gell-Mann matrices The Gell-Mann matrices, named for Murray Gell-Mann, are one possible representation of the infinitesimal generators of the special unitary group called SU(3). The Lie algebra of this group (a real Lie algebra in fact) has dimension eight and therefore it has some set with eight linearly independent generators, which can be written as $g\_i$, with ''i'' taking values from 1 to 8. ==Defining relations== These Lie Algebra elements obey the commutation relations :$(g\_j)\; =\; if^\; g\_k\; \backslash ,$ where a sum over the index ''k'' is implied. The structure constants $f^$ are completely antisymmetric in the three indices and have values :$f^\; =\; 1\; \backslash \; ,\; \backslash quad\; f^\; =\; f^\; =\; f^\; =\; f^\; =\; f^\; =\; f^\; =\; \backslash frac\; \backslash \; ,\; \backslash quad\; f^\; =\; f^\; =\; \backslash frac\; \backslash \; .$ Any set of Hermitian matrices which obey these relations qualifies. A particular choice of matrices is called a group representation, because any element of SU(3) can be written in the form $\backslash mathrm(i\; \backslash theta\_j\; g\_j)$, where $\backslash theta\_j$ are real numbers and a sum over the index ''j'' is implied. Given one representation, another may be obtained by an arbitrary unitary transformation, since that leaves the commutator unchanged. 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「Gell-Mann matrices」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.