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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 Spinor bundle ： ウィキペディア英語版 Spinor bundle In differential geometry, given a spin structure on a $n$-dimensional Riemannian manifold $(M,\; g),\backslash ,$ one defines the spinor bundle to be the complex vector bundle $\backslash pi\_\backslash colon\backslash to\; M\backslash ,$ associated to the corresponding principal bundle $\backslash pi\_\backslash colon\backslash to\; M\backslash ,$ of spin frames over $M$ and the spin representation of its structure group $\backslash ,$ is called a spinor field. ==Formal definition== Let $(,F\_)$ be a spin structure on a Riemannian manifold $(M,\; g),\backslash ,$ that is, an equivariant lift of the oriented orthonormal frame bundle $\backslash mathrm\; F\_(M)\backslash to\; M$ with respect to the double covering $\backslash rho\backslash colon\; \}(n).\backslash ,$ The spinor bundle $\backslash ,$ is defined 〔 page 53 〕 to be the complex vector bundle : $=\backslash times\_\backslash Delta\_n\backslash ,$ associated to the spin structure $$ via the spin representation $\backslash kappa\backslash colon\; (\backslash Delta\_n),\backslash ,$ where $()\backslash ,$ denotes the group of unitary operators acting on a Hilbert space $.\backslash ,$ It is worth noting that the spin representation $\backslash kappa$ is a faithful and unitary representation of the group $\{\backslash mathrm\; \{Spin\}\}(n)$.〔 pages 20 and 24〕 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「Spinor bundle」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.