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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 Spin tensor ： ウィキペディア英語版 Spin tensor :''Not to be confused with tensor products of spin representations.'' In mathematics, mathematical physics, and theoretical physics, the spin tensor is a quantity used to describe the rotational motion of particles in spacetime. The tensor has application in general relativity and special relativity, as well as quantum mechanics, relativistic quantum mechanics, and quantum field theory. The Euclidean group SE(d) of direct isometries is generated by translations and rotations. Its Lie algebra is written $\backslash mathfrak(d)$. This article uses Cartesian coordinates and tensor index notation. ==Background on Noether currents== The Noether current for translations in space is momentum, while the current for increments in time is energy. These two statements combine into one in spacetime: translations in spacetime, i.e. a displacement between two events, is generated by the four-momentum ''P''. Conservation of four-momentum is given by the continuity equation: :$\backslash partial\_\backslash nu\; T^=0\backslash ,,$ where $T^\; \backslash ,$ is the stress–energy tensor, and ∂ are partial derivatives that make up the four gradient (in non-Cartesian coordinates this must be replaced by the covariant derivative). Integrating over spacetime: :$\backslash int\; d^4\; x\; T^(\backslash vec,t)\; =\; P^\backslash mu$ gives the four-momentum vector at time ''t''. The Noether current for a rotation about the point ''y'' is given by a tensor of 3rd order, denoted $M^\_y$. Because of the Lie algebra relations :$M^\_y(x)=M^\_0(x)+y^\backslash alpha\; T^(x)-y^\backslash beta\; T^(x)\backslash ,,$ where the 0 subscript indicates the origin (unlike momentum, angular momentum depends on the origin), the integral: :$\backslash int\; d^4\; x\; M^\_0(\backslash vec,t)$ gives the angular momentum tensor $M^\; \backslash ,$ at time ''t''. 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「Spin tensor」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.