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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 field ： ウィキペディア英語版 Spinor field In differential geometry, given a spin structure on a ''n''-dimensional Riemannian manifold (''M, g'') a section of the spinor bundle S is called a spinor field. The complex vector bundle :$\backslash pi\_:\backslash to\; M\backslash ,$ is associated to the corresponding principal bundle :$\backslash pi\_:\backslash to\; M\backslash ,$ of spin frames over ''M'' via the spin representation of its structure group Spin(''n'') on the space of spinors Δ''n''. In particle physics particles with spin ''s'' are described by ''2s''-dimensional spinor field, where ''s'' is a integer or a half-integer. Fermions are described by spinor field, while bosons by tensor field. ==Formal definition== Let (P, ''F''P) be a spin structure on a Riemannian manifold (''M, g'') that is, an equivariant lift of the oriented orthonormal frame bundle $\backslash mathrm\; F\_(M)\backslash to\; M$ with respect to the double covering $\backslash rho:\; \}(n)\backslash ,.$ One usually defines the spinor bundle $\backslash pi\_:\backslash to\; M\backslash ,$ to be the complex vector bundle :$=\backslash times\_\backslash Delta\_n\backslash ,$ associated to the spin structure P via the spin representation $\backslash kappa:\; (\backslash Delta\_n),\backslash ,$ where U(W) denotes the group of unitary operators acting on a Hilbert space W. A spinor field is defined to be a section of the spinor bundle S, i.e., a smooth mapping $\backslash psi\; :\; M\; \backslash to\; \backslash ,$ such that $\backslash pi\_\backslash circ\backslash psi:\; M\backslash to\; M\backslash ,$ is the identity mapping id''M'' of ''M''. 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 field」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.