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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 twistor theory ： ウィキペディア英語版 twistor theory In theoretical and mathematical physics, twistor theory maps the geometric objects of conventional 3+1 space-time (Minkowski space) into geometric objects in a 4-dimensional space endowed with a Hermitian form of signature (2,2). This space is called twistor space, and its complex valued coordinates are called "twistors." Twistor theory was first proposed by Roger Penrose in 1967,〔Penrose, R. (1967) "Twistor algebra," ''J. Math. Phys.'' 8: 345.〕 as a possible path to a theory of quantum gravity. The twistor approach is especially natural for solving the equations of motion of massless fields of arbitrary spin. In 2003, Edward Witten〔Witten, E. (2004) "(Perturbative gauge theory as a string theory in twistor space, )" ''Commun. Math. Phys.'' 252: 189–258.〕 proposed uniting twistor and string theory by embedding the topological B model of string theory in twistor space. His objective was to model certain Yang–Mills amplitudes. The resulting model has come to be known as twistor string theory (read below). Simone Speziale and collaborators have also applied it to loop quantum gravity.〔http://arxiv.org/abs/1006.0199〕 ==Details== Twistor theory is unique to 4D Minkowski space and the (2,2) signature, and does not generalize to other dimensions or signatures. At the heart of twistor theory lies the isomorphism between the conformal group Spin(4,2) and SU(2,2), which is the group of unitary transformations of determinant 1 over a four-dimensional complex vector space that leave invariant a Hermitian form of signature (2,2), see classical group. * $\backslash mathbb^6$ is the real 6D vector space corresponding to the vector representation of Spin(4,2). * $\backslash mathbf\backslash mathbb^5$ is the real 5D projective representation corresponding to the equivalence class of nonzero points in $\backslash mathbb^6$ under scalar multiplication. * $\backslash mathbb^c$ corresponds to the subspace of $\backslash mathbf\backslash mathbb^5$ corresponding to vectors of zero norm. This is conformally compactified Minkowski space. * $\backslash mathbb$ is the 4D complex Weyl spinor representation, called twistor space. It has an invariant Hermitian sesquilinear norm of signature (2,2). * $\backslash mathbb$ is a 3D complex manifold corresponding to projective twistor space. * $\backslash mathbb^+$ is the subspace of $\backslash mathbb$ corresponding to projective twistors with positive norm (the sign of the norm, but not its absolute value is projectively invariant). This is a 3D complex manifold. * $\backslash mathbb$ is the subspace of $\backslash mathbb$ consisting of null projective twistors (zero norm). This is a real-complex manifold (i.e., it has 5 real dimensions, with four of the real dimensions having a complex structure making them two complex dimensions). * $\backslash mathbb^-$ is the subspace of $\backslash mathbb$ of projective twistors with negative norm. $\backslash mathbb^c$, $\backslash mathbb^+$, $\backslash mathbb$ and $\backslash mathbb^-$ are all homogeneous spaces of the conformal group. $\backslash mathbb^c$ admits a conformal metric (i.e., an equivalence class of metric tensors under Weyl rescalings) with signature (+++−). Straight null rays map to straight null rays under a conformal transformation and there is a unique canonical isomorphism between null rays in $\backslash mathbb^c$ and points in $\backslash mathbb$ respecting the conformal group. In $\backslash mathbb^c$, it is the case that positive and negative frequency solutions cannot be locally separated. However, this is possible in twistor space. $\backslash mathbb^+\; \backslash simeq\; \backslash mathrm(2,2)/\backslash left(\backslash mathrm(2,1)\; \backslash times\; \backslash mathrm(1)\; \backslash right)$ 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「twistor theory」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.