| 词条 | Twisted geometries |
| 释义 |
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.[1][2][3] A twisted geometry can be visualized as collections of polyhedra dual to the nodes of the spin network's graph.[4] 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 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.[5][6] References1. ^{{cite journal | author=L. Freidel and S. Speziale | title=Twisted geometries: A geometric parametrisation of SU(2) phase space | journal=Phys. Rev. D | year=2010 | volume=82 | issue=8 | pages=084040 | doi=10.1103/PhysRevD.82.084040|arxiv = 1001.2748 |bibcode = 2010PhRvD..82h4040F }} 2. ^{{cite journal | author=C. Rovelli and S. Speziale | title=On the geometry of loop quantum gravity on a graph | journal=Phys. Rev. D | year=2010 | volume=82 | issue=4 | pages=044018 | doi=10.1103/PhysRevD.82.044018|arxiv = 1005.2927 |bibcode = 2010PhRvD..82d4018R }} 3. ^{{cite journal | author=E. R. Livine and J. Tambornino | title=Spinor Representation for Loop Quantum Gravity | journal=J. Math. Phys. | year=2012 | volume=53 | issue=1 | pages=012503 | doi=10.1063/1.3675465|arxiv = 1105.3385 |bibcode = 2012JMP....53a2503L }} 4. ^{{cite journal | author=E. Bianchi, P. Dona and S. Speziale | title=Polyhedra in loop quantum gravity | journal=Phys. Rev. D | year=2011 | volume=83 | issue=4 | pages=044035 | doi=10.1103/PhysRevD.83.044035|arxiv = 1009.3402 |bibcode = 2011PhRvD..83d4035B }} 5. ^{{cite journal | author=L. Freidel and S. Speziale | title=From twistors to twisted geometries | journal=Phys. Rev. D | year=2010 | volume=82 | issue=8 | pages=084041 | doi=10.1103/PhysRevD.82.084041|arxiv = 1006.0199 |bibcode = 2010PhRvD..82h4041F }} 6. ^{{cite journal | author=S. Speziale and Wolfgang M. Wieland | title=The twistorial structure of loop-gravity transition amplitudes | journal=Phys. Rev. D | year=2012 | volume=86 | issue=12 | pages=124023 | doi=10.1103/PhysRevD.86.124023|arxiv = 1207.6348 |bibcode = 2012PhRvD..86l4023S }} External links{{quantum-stub}} 4 : Loop quantum gravity|Theories of gravitation|Physics beyond the Standard Model|Quantum field theory |
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