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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 Clebsch–Gordan coefficients for SU(3) ： ウィキペディア英語版 Clebsch–Gordan coefficients for SU(3) In mathematical physics, Clebsch–Gordan coefficients are the expansion coefficients of total angular momentum eigenstates in an uncoupled tensor product basis. Mathematically, they specify the decomposition of the tensor product of two irreducible representations into a direct sum of irreducible representations, where the type and the multiplicities of these irreducible representations are known abstractly. The name derives from the German mathematicians Alfred Clebsch (1833–1872) and Paul Gordan (1837–1912), who encountered an equivalent problem in invariant theory. Generalization to SU(3) of Clebsch–Gordan coefficients is useful because of their utility in characterizing hadronic decays, where a flavor-SU(3) symmetry exists (the Eightfold Way (physics)) that connects the three light quarks: up, down, and strange. ==Groups== (詳細はbinary operation ( *) (often called a 'multiplication'), satisfying the following properties: # Closure: For every pair of elements $x$ and $y$ in $G$, the ''product'' $x$ *y is also in $G$ ( in symbols, for every two elements $x,y\backslash in\; G,x$ *y is also in $G.$ # Associativity: For every $x$ and $y$ and $z$ in $G$, both $(x$ *y) *z and $x$ *(y *z) result with the same element in $G$ ( in symbols, $(x$ *y) *z=x *(y *z) for every $x,y$, and $z\; \backslash in\; G$). # Existence of identity: There must be an element ( say $e$ ) in $G$ such that product any element of $G$ with $e$ make no change to the element ( in symbols, $x$ *e=e *x= x for every $x\backslash in\; G$). # Existence of inverse: For each element ($x$ ) in $G$, there must be an element $y$ in $G$ such that product of $x$ and $y$ is the identity element $e$ ( in symbols, for each $x\backslash in\; G$ there is a $y\; \backslash in\; G$ such that $x$ *y=y *x=e for every;$x\backslash in\; G$). # Commutative: In addition to the above four, if it so happens that $$ \forall x,y\in G, $x$ *y=y *x, then the group is called an Abelian Group. Otherwise it is called a non-Abelian group. 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「Clebsch–Gordan coefficients for SU(3)」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.