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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 Belinfante–Rosenfeld stress–energy tensor ： ウィキペディア英語版 Belinfante–Rosenfeld stress–energy tensor In mathematical physics, the Belinfante–Rosenfeld tensor is a modification of the energy–momentum tensor that is constructed from the canonical energy–momentum tensor and the spin current so as to be symmetric yet still conserved. In a classical or quantum local field theory, the generator of Lorentz transformations can be written as an integral : $M\_\; =\; \backslash int\; d^3x\; \backslash ,\; \_$ of a local current : $\_=\; (x\_\backslash nu\; \_\backslash lambda\; -\; x\_\backslash lambda\; \_\backslash nu)+\; \_.$ Here $\_\backslash lambda$ is the canonical Noether energy–momentum tensor, and $$ is the contribution of the intrinsic (spin) angular momentum. Local conservation of angular momentum : $\backslash partial\_\backslash mu\; \_=0\; \backslash ,$ requires that : $\backslash partial\_\backslash mu\; \_=T\_-T\_.$ Thus a source of spin-current implies a non-symmetric canonical energy–momentum tensor. The Belinfante–Rosenfeld tensor is a modification of the energy momentum tensor : $T\_B^\; =\; T^\; +\backslash frac\; 12\; \backslash partial\_\backslash lambda(S^+S^-S^)$ that is constructed from the canonical energy momentum tensor and the spin current $$ so as to be symmetric yet still conserved. An integration by parts shows that : $M^\; =\; \backslash int\; (x^\backslash nu\; T^\_B\; -\; x^\backslash lambda\; T^\_B)\; \backslash ,\; d^3x,$ and so a physical interpretation of Belinfante tensor is that it includes the "bound momentum" associated with gradients of the intrinsic angular momentum. In other words, the added term is an analogue of the $\_\backslash text=\; \backslash nabla\backslash times\; \backslash bold$ "bound current" associated with a magnetization density $$. The curious combination of spin-current components required to make $T\_B^$ symmetric and yet still conserved seems totally ''ad hoc'', but it was shown by both Rosenfeld and Belinfante that the modified tensor is precisely the symmetric Hilbert energy–momentum tensor that acts as the source of gravity in general relativity. Just as it is the sum of the bound and free currents that acts as a source of the magnetic field, it is the sum of the bound and free energy–momentum that acts as a source of gravity. Weinberg defines the Belinfante tensor as : :$T^=\backslash eta^\backslash mathcal-\backslash frac\backslash partial^\backslash nu\backslash Psi^\backslash ell$ and $\backslash mathcal^,\backslash mathcal^"\; TITLE="\backslash mathcal^,\backslash mathcal^">)=i\backslash mathcal^\backslash eta^-i\backslash mathcal^\backslash eta^-i\backslash mathcal^\backslash eta^+i\backslash mathcal^\backslash eta^$. ==References== 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「Belinfante–Rosenfeld stress–energy 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.