翻訳と辞書 Words near each other ・ Four-handed ・ Four-horned antelope ・ Four-hour target in emergency departments ・ Four-in-hand (carriage) ・ Four-in-hand knot ・ Four-leaf clover ・ Four-letter abbreviation ・ Four-letter word ・ Four-line wrasse ・ Four-lined snake ・ Four-lined wrasse ・ Four-Mations ・ Four-minute mile ・ Four-minute warning ・ Four-Mod ・ Four-momentum ・ Four-part harmony ・ Four-phase logic ・ Four-Phase Systems ・ Four-Pillars Hotels ・ Four-player chess ・ Four-point play ・ Four-pointer ・ Four-poster bed ・ Four-Power Authorities ・ Four-Power Pact ・ Four-Power Treaty ・ Four-quadrant gate ・ Four-quadrant movie ・ Four-seam fastball 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 Four-momentum ： ウィキペディア英語版 Four-momentum In special relativity, four-momentum is the generalization of the classical three-dimensional momentum to four-dimensional spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime. The contravariant four-momentum of a particle with energy and three-momentum , where is the particles and the Lorentz factor, is :$$ p = (p^0 , p^1 , p^2 , p^3 ) = \left( , p_x , p_y , p_z\right). The quantity of above is ordinary non-relativistic momentum of the particle and its rest mass. The four-momentum is useful in relativistic calculations because it is a Lorentz vector. This means that it is easy to keep track of how it transforms under Lorentz transformations. The above definition applies under the coordinate convention that . Some authors use the convention , which yields a modified definition with . It is also possible to define covariant four-momentum where the sign of the energy is reversed. == Minkowski norm == Calculating the Minkowski norm of the four-momentum gives a Lorentz invariant quantity equal (up to factors of the speed of light ) to the square of the particle's proper mass: :$p\; \backslash cdot\; p\; =\; p^\backslash mu\; p\_\backslash mu\; =\; \backslash eta\_\; p^\backslash mu\; p^\backslash nu\; =\; -\; +\; |\backslash mathbf\; p|^2\; =\; -m^2c^2$ where we use the convention that : 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 \end\right ) is the metric tensor of special relativity. The fact that the norm is negative reflects that the momentum is a timelike for massive particles. The Minkowski norm is Lorentz invariant, meaning its value is not changed by Lorentz transformations/boosting into different frames of reference. More generally, for any two and , the quantity is invariant. 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「Four-momentum」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.