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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 Supersymmetry as a quantum group ： ウィキペディア英語版 Supersymmetry as a quantum group The concept in theoretical physics of supersymmetry can be reinterpreted in the language of noncommutative geometry and quantum groups. In particular, it involves a mild form of noncommutativity, namely supercommutativity. ==Unitary (-1)''F'' operator== Following is the essence of supersymmetry, which is encapsulated within the following minimal quantum group. We have the two dimensional Hopf algebra generated by (-1)F subject to :$^2=1$ with the counit :$\backslash epsilon((-1)^F)=1$ and the coproduct :$\backslash Delta\; (-1)^F=(-1)^F\; \backslash otimes\; (-1)^F$ and the antipode :$S(-1)^F=(-1)^F$ Thus far, there is nothing supersymmetric about this Hopf algebra at all; it is isomorphic to the Hopf algebra of the two element group $\backslash mathbb\_2$. Supersymmetry comes in when introducing the nontrivial quasitriangular structure :$\backslash mathcal=\backslash frac\backslash left(1\; \backslash otimes\; 1\; +\; (-1)^F\; \backslash otimes\; 1\; +\; 1\; \backslash otimes\; (-1)^F\; -\; (-1)^F\; \backslash otimes\; (-1)^F\backslash right)$ where +1 eigenstates of (-1)''F'' are called bosons and -1 eigenstates are called fermions. This describes a fermionic braiding; don't pick up a phase factor when interchanging two bosons or a boson and a fermion, but multiply by -1 when interchanging two fermions. This provides the essence of the boson/fermion distinction. 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「Supersymmetry as a quantum group」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.