翻訳と辞書 Words near each other ・ Super-imperialism ・ Super-injunctions in English law ・ Super-insulation systems ・ Super-iron battery ・ Super-Jupiter ・ Super-Kamiokande ・ Super-logarithm ・ Super-LOTIS ・ Super-LumiNova ・ Super-majority amendment ・ Super-Markets Arvanitidis ・ Super-Neutron ・ Super-Patriot ・ Super-Patriot (Marvel Comics) ・ Super-Pharm ・ Super-Poincaré algebra ・ Super-Poissonian distribution ・ Super-Poulet number ・ Super-prefectures of Greece ・ Super-prime ・ Super-proportional division ・ Super-Rabbit ・ Super-recursive algorithm ・ Super-resolution imaging ・ Super-resolution microscopy ・ Super-resolution optical fluctuation imaging ・ Super-Sargasso Sea ・ Super-Science Fiction ・ Super-seeding ・ Super-server Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Super-Poincaré algebra ： ウィキペディア英語版 Super-Poincaré algebra In theoretical physics, a super-Poincaré algebra is an extension of the Poincaré algebra to incorporate supersymmetry, a relation between bosons and fermions. They are examples of supersymmetry algebras (without central charges or internal symmetries), and are Lie superalgebras. Thus a super-Poincaré algebra is a Z2 graded vector space with a graded Lie bracket such that the even part is a Lie algebra containing the Poincaré algebra, and the odd part is built from spinors on which there is an anticommutation relation with values in the even part. The simplest supersymmetric extension of the Poincaré algebra contains two Weyl spinors with the following anti-commutation relation: :$\backslash \}\backslash \}\; =\; 2\_$ as: :$\backslash \; =\; 2g^$ and :$\backslash sigma^=\backslash frac(\backslash gamma^\backslash mu,\backslash gamma^\backslash nu)$ This then gives the full algebra〔P. van Nieuwenhuizen, Phys. Rep. 68, 189 (1981)〕 :$(M^\; ,\; Q\_\backslash alpha)\; =\; \backslash frac\; (\; \backslash sigma^)\_\backslash alpha^\backslash beta\; Q\_\backslash beta$ $(Q\_\backslash alpha\; ,\; P^\backslash mu)\; =\; 0$ $\backslash \}\; \backslash \}\; =\; 2\; (\; \backslash sigma^\backslash mu\; )\_\{\backslash alpha\; \backslash dot\{\backslash beta\}\}\; P\_\backslash mu$ with the addition of the normal Poincaré algebra. It is a closed algebra since all Jacobi identities are satisfied and can have since explicit matrix representations. Following this line of reasoning will lead to Supergravity. ==SUSY in 3 + 1 Minkowski spacetime== In 3+1 Minkowski spacetime, the Haag-Lopuszanski-Sohnius theorem states that the SUSY algebra with ''N'' spinor generators is as follows. The even part of the V )\otimes(V^ * ) to the ideal (ring theory)" TITLE="star Lie superalgebra is the direct sum of the Poincaré algebra and a reductive Lie algebra ''B'' (such that its self-adjoint part is the tangent space of a real compact Lie group). The odd part of the algebra would be :$\backslash left(\backslash frac,0\backslash right)\backslash otimes\; V\backslash oplus\backslash left(0,\backslash frac\backslash right)\backslash otimes\; V^$ * where $(1/2,0)$ and $(0,1/2)$ are specific representations of the Poincaré algebra. Both components are conjugate to each other under the * conjugation. ''V'' is an ''N''-dimensional complex representation of ''B'' and ''V'' * is its dual representation. The Lie bracket for the odd part is given by a symmetric equivariant pairing on the odd part with values in the even part. In particular, its reduced intertwiner from $(V)\backslash otimes(V^$ * ) to the ideal (ring theory)">ideal of the Poincaré algebra generated by translations is given as the product of a nonzero intertwiner from $(\backslash frac,0)\backslash otimes(0,\backslash frac)$ to (1/2,1/2). The "contraction intertwiner" from $V\backslash otimes\; V^$ * to the trivial representation and the reduced intertwiner from $(V)\backslash otimes\; (V)$ is the product of a (antisymmetric) intertwiner from (1/2,0) squared to (0,0) and an antisymmetric intertwiner ''A'' from $N^2$ to ''B''. * conjugate it to get the corresponding case for the other half. 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「Super-Poincaré 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.