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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. * is the real 6D vector space corresponding to the vector representation of Spin(4,2). * is the real 5D projective representation corresponding to the equivalence class of nonzero points in under scalar multiplication. * corresponds to the subspace of corresponding to vectors of zero norm. This is conformally compactified Minkowski space. * is the 4D complex Weyl spinor representation, called twistor space. It has an invariant Hermitian sesquilinear norm of signature (2,2). * is a 3D complex manifold corresponding to projective twistor space. * is the subspace of 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. * is the subspace of 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). * is the subspace of of projective twistors with negative norm. , , and are all homogeneous spaces of the conformal group. 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 and points in respecting the conformal group. In , it is the case that positive and negative frequency solutions cannot be locally separated. However, this is possible in twistor space. 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
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