翻訳と辞書 Words near each other ・ SpaceShipOne flight 16P ・ SpaceShipOne Flight 17P ・ SpaceShipThree ・ SpaceShipTwo ・ SpaceShipTwo, Serial Number Two ・ SpaceSniffer ・ Spacestation Pheta ・ SpaceStationSim ・ Spacesuits in fiction ・ Spaceteam ・ SpaceTEC National Resource Center for Aerospace Technical Education ・ SpaceTime ・ Spacetime ・ Spacetime (disambiguation) ・ SpaceTime (software) ・ Spacetime algebra ・ Spacetime Studios ・ Spacetime symmetries ・ Spacetime topology ・ Spacetime triangle diagram technique ・ Spacetoon ・ Spacetoon English ・ Spacetoon Radio ・ Spaceturk ・ SpaceUp ・ SpaceVets ・ Spacewalk (software) ・ Spacewar ・ Spacewar (video game) ・ Spaceward Ho! 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 Spacetime algebra ： ウィキペディア英語版 Spacetime algebra In mathematical physics, spacetime algebra (STA) is a name for the Clifford algebra ''C''ℓ1,3(R), or equivalently the geometric algebra ''G''4 = ''G''(M4), which can be particularly closely associated with the geometry of special relativity and relativistic spacetime. It is a vector space allowing not just vectors, but also bivectors (directed quantities associated with particular planes, such as areas, or rotations) or multivectors (quantities associated with particular hyper-volumes) to be combined, as well as rotated, reflected, or Lorentz boosted. It is also the natural parent algebra of spinors in special relativity. These properties allow many of the most important equations in physics to be expressed in particularly simple forms, and can be very helpful towards a more geometric understanding of their meanings. ==Structure== The spacetime algebra is built up from combinations of one time-like basis vector $\backslash gamma\_0$ and three orthogonal space-like vectors, $\backslash$, under the multiplication rule :$\backslash gamma\_\backslash mu\; \backslash gamma\_\backslash nu\; +\; \backslash gamma\_\backslash nu\; \backslash gamma\_\backslash mu\; =\; 2\; \backslash eta\_$ where $\backslash eta\_\; \backslash ,$ is the Minkowski metric with signature (+ − − −) Thus $\backslash gamma\_0^2\; =$, $\backslash gamma\_1^2\; =\; \backslash gamma\_2^2\; =\; \backslash gamma\_3^2\; =$, otherwise $\backslash displaystyle\; \backslash gamma\_\backslash mu\; \backslash gamma\_\backslash nu\; =\; -\; \backslash gamma\_\backslash nu\; \backslash gamma\_\backslash mu$. The basis vectors $\backslash gamma\_k$ share these properties with the Dirac matrices, but no explicit matrix representation is utilized in STA. This generates a basis of one scalar $\backslash$, four vectors $\backslash$, six bivectors $\backslash$, four pseudovectors $\backslash$ and one pseudoscalar $\backslash$, where $i=\backslash gamma\_0\; \backslash gamma\_1\; \backslash gamma\_2\; \backslash gamma\_3$. 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「Spacetime algebra」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.