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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 Grassmann integral ： ウィキペディア英語版 Grassmann integral In mathematical physics, a Grassmann integral, or, more correctly, Berezin integral, is a way to define integration for functions of Grassmann variables. It is not an integral in the Lebesgue sense; it is called integration because it has analogous properties and since it is used in physics as a sum over histories for fermions, an extension of the path integral. The technique was invented by the Russian mathematician Felix Berezin and developed in his textbook.〔A. Berezin, ''The Method of Second Quantization'', Academic Press, (1966)〕 Some earlier insights were made by the physicist David John Candlin in 1956. ==Definition== The ''Berezin integral'' is defined to be a linear functional : $\backslash int\; ()\; \backslash ,\; d\backslash theta\; =\; a\backslash int\; f(\backslash theta)\; \backslash ,\; d\backslash theta\; +\; b\backslash int\; g(\backslash theta)\; \backslash ,\; d\backslash theta$ where we define : $\backslash int\; \backslash theta\; \backslash ,\; d\backslash theta\; =\; 1$ : $\backslash int\; \backslash ,\; d\backslash theta\; =\; 0$ so that : : $\backslash int\; \backslash frac\backslash partialf(\backslash theta)\backslash ,d\backslash theta\; =\; 0.$ These properties define the integral uniquely. : $\backslash int\; (a\backslash theta+b)\backslash ,\; d\backslash theta\; =\; a.$ This is the most general function, because every homogeneous function of one Grassmann variable is either constant or linear. 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「Grassmann integral」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.