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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 Curtright field ： ウィキペディア英語版 Curtright field In theoretical physics, the Curtright field (named after Thomas Curtright) is a tensor quantum field of mixed symmetry, whose gauge-invariant dynamics are dual to those of the general relativistic graviton in higher (''D''>4) spacetime dimensions. Or at least this holds for the linearized theory.〔West, P. (2014). "Dual gravity and E11", arXiv:1411.0920〕 For the full nonlinear theory, less is known. Several difficulties arise when interactions of mixed symmetry fields are considered, but at least in situations involving an infinite number of such fields (notably string theory) these difficulties are not insurmountable. In four spacetime dimensions, the field is not dual to the graviton, if massless, but it can be used to describe ''massive'', pure spin 2 quanta. Similar descriptions exist for other massive higher spins, in ''D''≥4. The simplest example of the linearized theory is given by a rank three Lorentz tensor $T\_$ whose indices carry the permutation symmetry of the Young diagram corresponding to the integer partition 3=2+1. That is to say, $T\_=T\_$ and $T\_=0$ where indices in square brackets are totally antisymmetrized. The corresponding field strength for $T\_$ is $F\_=3\backslash partial\_T\_T\_.$ This has a nontrivial trace $F\_=\backslash eta^F\_$ where $\backslash eta^$ is the Minkowski metric with signature (+,−,−,...). The action for $T\_$ in ''D'' spacetime dimensions is bilinear in the field strength and its trace. :$S=\backslash frac\; \backslash int\; d^x\; (F\_F^-3F\_F^).$ This action is gauge invariant, assuming there is zero net contribution from any boundaries, while the field strength itself is not. The gauge transformation in question is given by :$\backslash delta\; T\_=\backslash partial\_S\_S\_+\backslash partial\_A\_A\_-\backslash partial\_A\_$ where ''S'' and ''A'' are arbitrary symmetric and antisymmetric tensors, respectively. An infinite family of mixed symmetry gauge fields arises, formally, in the zero tension limit of string theory, especially if ''D''>4. Such mixed symmetry fields can also be used to provide alternate local descriptions for massive particles, either in the context of strings with nonzero tension, or else for individual particle quanta without reference to string theory. ==See also== * Kalb–Ramond field * p-form electrodynamics 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「Curtright field」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.