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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 Poisson superbracket ： ウィキペディア英語版 Poisson superalgebra In mathematics, a Poisson superalgebra is a Z2-graded generalization of a Poisson algebra. Specifically, a Poisson superalgebra is an (associative) superalgebra ''A'' with a Lie superbracket :$()\; :\; A\backslash otimes\; A\backslash to\; A$ such that (''A'', ()) is a Lie superalgebra and the operator :$()\; :\; A\backslash to\; A$ is a superderivation of ''A'': :$()\; =\; ()z\; +\; (-1)^y().\backslash ,$ A supercommutative Poisson algebra is one for which the (associative) product is supercommutative. This is one possible way of "super"izing the Poisson algebra. This gives the classical dynamics of fermion fields and classical spin-1/2 particles. The other is to define an antibracket algebra instead. This is used in the BRST and Batalin-Vilkovisky formalism. == Examples == * If ''A'' is any associative Z2 graded algebra, then, defining a new product () (which is called the super-commutator) by ():=xy-(-1)|x||y|yx for any pure graded x, y turns ''A'' into a Poisson superalgebra. 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「Poisson superalgebra」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.