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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 Superconformal algebra ： ウィキペディア英語版 Superconformal algebra In theoretical physics, the superconformal algebra is a graded Lie algebra or superalgebra that combines the conformal algebra and supersymmetry. It generates the superconformal group in some cases (In two Euclidean dimensions, the Lie superalgebra does not generate any Lie supergroup.). In two dimensions, the superconformal algebra is infinite-dimensional. In higher dimensions, there is a finite number of known examples of superconformal algebras. == Superconformal algebra in 3+1D == According to,〔 〕 the $\backslash mathcal=1$ superconformal algebra in 3+1D is given by the bosonic generators $P\_\backslash mu$, $D$, $M\_$, $K\_\backslash mu$, the U(1) R-symmetry $A$, the SU(N) R-symmetry $T^i\_j$ and the fermionic generators $Q^$, $\backslash overline^\_i$, $S^\backslash alpha\_i$ and $$. Here, $\backslash mu,\backslash nu,\backslash rho,\backslash dots$ denote spacetime indices; $\backslash alpha,\backslash beta,\backslash dots$ left-handed Weyl spinor indices; $\backslash dot\backslash alpha,\backslash dot\backslash beta,\backslash dots$ right-handed Weyl spinor indices; and $i,j,\backslash dots$ the internal R-symmetry indices. The Lie superbrackets of the bosonic conformal algebra are given by :$()=\backslash eta\_M\_-\backslash eta\_M\_+\backslash eta\_M\_-\backslash eta\_M\_$ :$()=\backslash eta\_P\_\backslash mu-\backslash eta\_P\_\backslash nu$ :$()=\backslash eta\_K\_\backslash mu-\backslash eta\_K\_\backslash nu$ :$()=0$ :$()=-P\_\backslash rho$ :$()=+K\_\backslash rho$ :$()=-2M\_+2\backslash eta\_D$ :$()=0$ :$()=0$ where η is the Minkowski metric; while the ones for the fermionic generators are: :$\backslash left\backslash \_\; =\; 2\; \backslash delta^j\_i\; \backslash sigma^\_\; =\; \backslash left\backslash \; \backslash right\backslash \}\; =\; 0$ :$\backslash left\backslash \_\; \backslash right\backslash \}\; =\; 2\; \backslash delta^i\_j\; \backslash sigma^\_\; =\; \backslash left\backslash \; \backslash right\backslash \}\; =\; 0$ :$\backslash left\backslash \; =$ :$\backslash left\backslash \; =\; \backslash left\backslash \; =\; 0$ The bosonic conformal generators do not carry any R-charges, as they commute with the R-symmetry generators: :$()=()=()=()=0$ :$()=()=()=()=0$ But the fermionic generators do carry R-charge: :$()=-\backslash fracQ$ :$()=\backslash frac\backslash overline$ :$()=\backslash fracS$ :$()=-\backslash frac\backslash overline$ :$()=\; -\; \backslash delta^i\_k\; Q\_j$ :$()=\; \backslash delta^k\_j\; \_k"\; TITLE="T^i\_j,\backslash overline\_k">)=\; -\; \backslash delta^i\_k\; \backslash overline\_j$ Under bosonic conformal transformations, the fermionic generators transform as: :$()=-\backslash fracQ$ :$()=-\backslash frac\backslash overline$ :$()=\backslash fracS$ :$()=\backslash frac\backslash overline$ :$()=()=0$ :$()=()=0$ 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「Superconformal algebra」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.