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Twisted geometries are discrete geometries that plays a role in loop quantum gravity and spin foam models, where they appear in the semiclassical limit of spin networks.〔 (eprint ) 〕 〔 (eprint )〕〔 (eprint ) 〕 A twisted geometry can be visualized as collections of polyhedra dual to the nodes of the spin network's graph.〔 (eprint )〕 Intrinsic and extrinsic curvatures are defined in a manner similar to Regge calculus, but with the generalisation of including a certain type of metric discontinuities: the face shared by two adjacent polyhedra has a unique area, but its shape can be different. This is a consequence of the quantum geometry of spin networks: ordinary Regge calculus is "too rigid" to account for all the geometric degrees of freedom described by a the semiclassical limit of a spin network. The name twisted geometry captures the relation between these additional degrees of freedom and the off-shell presence of torsion in the theory, but also the fact that this classical description can be derived from Twistor theory, by assigning a pair of twistors to each link of the graph, and suitably constraining their helicities and incidence relations.〔 (eprint ) 〕 〔 (eprint )〕 == 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「Twisted geometries」の詳細全文を読む スポンサード リンク
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