翻訳と辞書 Words near each other ・ Tetragonoderus fimbriatus ・ Tetracycline ・ Tetracycline antibiotics ・ Tetracycline litigation ・ Tetracycline-controlled transcriptional activation ・ Tetracyclopropylmethane ・ Tetracynodon ・ Tetracystis ・ Tetrad ・ Tetrad (area) ・ Tetrad (astronomy) ・ Tetrad (genetics) ・ Tetrad (Greek philosophy) ・ Tetrad (index notation) ・ Tetrad (music) ・ Tetrad formalism ・ Tetrad Islands ・ Tetrad of media effects ・ Tetrad test ・ Tetradactylus ・ Tetradecagon ・ Tetradecahedron ・ Tetradecane ・ Tetradecathlon ・ Tetradecylthioacetic acid ・ Tetradenia ・ Tetradesmus ・ Tetradia lophoptera ・ Tetradic Palatini action ・ Tetradifon Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Tetrad formalism ： ウィキペディア英語版 Tetrad formalism The tetrad formalism is an approach to general relativity that replaces the choice of a coordinate basis by the less restrictive choice of a local basis for the tangent bundle, i.e. a locally defined set of four linearly independent vector fields called a tetrad. In the tetrad formalism all tensors are represented in terms of a chosen basis. (When generalised to other than four dimensions this approach is given other names, see Cartan formalism.) As a formalism rather than a theory, it does not make different predictions but does allow the relevant equations to be expressed differently. The advantage of the tetrad formalism over the standard coordinate-based approach to general relativity lies in the ability to choose the tetrad basis to reflect important physical aspects of the spacetime. The abstract index notation denotes tensors as if they were represented by their coefficients with respect to a fixed local tetrad. Compared to a completely coordinate free notation, which is often conceptually clearer, it allows an easy and computationally explicit way to denote contractions. ==Mathematical formulation== In the tetrad formalism, a tetrad basis is chosen: a set of four independent vector fields $\backslash scriptstyle\backslash ^\; \backslash partial\_\backslash mu\backslash \}\_$ that together span the 4D vector tangent space at each point in spacetime. Dually, a tetrad determines (and is determined by) a dual co-tetrad—a set of four independent covectors (1-forms) $\backslash scriptstyle\backslash \_\; dx^\backslash mu\backslash \}\_$ such that :$e^\; (e\_)\; =\; e^\_\backslash mu\; e^\backslash mu\_\; =\; \backslash delta^\_,$ where $\backslash delta^\_$ is the Kronecker delta. A tetrad is usually specified by its coefficients $e\_^$ with respect to a coordinate basis, despite the fact that the choice of a tetrad does not actually require the additional choice of a set of (local) coordinates $x^\backslash mu$. From a mathematical point of view, the four vector fields $\backslash scriptstyle\backslash \_$ define a section of the frame bundle i.e. a parallelization of $\backslash scriptstyle\; M$ which is equivalent to an isomorphism $\backslash scriptstyle\; TM\; \backslash cong\; M\backslash times$. Since not every manifold is parallelizable, a tetrad can generally only be chosen locally. All tensors of the theory can be expressed in the vector and covector basis, by expressing them as linear combinations of members of the (co)tetrad. For example, the spacetime metric itself can be transformed from a coordinate basis to the tetrad basis. Popular tetrad bases include orthonormal tetrads and null tetrads. Null tetrads are composed of light cone vectors, so are used frequently in problems dealing with radiation, and are the basis of the Newman–Penrose formalism and the GHP formalism. 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「Tetrad formalism」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.