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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 Kontsevich quantization formula ： ウィキペディア英語版 Kontsevich quantization formula In mathematics, the Kontsevich quantization formula describes how to construct a generalized ★-product operator algebra from a given arbitrary Poisson manifold. This operator algebra amounts to the deformation quantization of the corresponding Poisson algebra. It is due to Maxim Kontsevich.〔M. Kontsevich (2003), (''Deformation Quantization of Poisson Manifolds'' ), ''Letters of Mathematical Physics'' 66, pp. 157–216.〕 ==Deformation quantization of a Poisson algebra== Given a Poisson algebra , a deformation quantization is an associative unital product ★ on the algebra of formal power series in , subject to the following two axioms, :$\backslash begin$ f *g &=fg+\mathcal(\hbar)\\ (\hbar^2) \end If one were given a Poisson manifold , one could ask, in addition, that :$f$ *g=fg+\sum_^\infty \hbar^kB_k(f\otimes g), where the are linear bidifferential operators of degree at most . Two deformations are said to be equivalent iff they are related by a gauge transformation of the type, :$\backslash begin$ D: A\hbar\to A\hbar \\ \sum_^\infty \hbar^k f_k \mapsto \sum_^\infty \hbar^k f_k +\sum_ D_n(f_k)\hbar^ \end where are differential operators of order at most . The corresponding induced ★-product, ★′, is then :$f\backslash ,\text{'}\backslash ,g\; =\; D\; \backslash left\; (\; \backslash left\; (D^f\; \backslash right\; )$ * \left (D^g \right ) \right ). For the archetypal example, one may well consider Groenewold's original "Moyal–Weyl" ★-product. 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「Kontsevich quantization formula」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.