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2010

From twistors to twisted geometries

Freidel, Laurent, Speziale, Simone

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In a previous paper we showed that the phase space of loop quantum gravity on a fixed graph can be parametrized in terms of twisted geometries, quantities describing the intrinsic and extrinsic discrete geometry of a cellular decomposition dual to the graph.

Here we unravel the origin of the phase space from a geometric interpretation of twistors.

From twistors to twisted geometries · Around

Built on

R. Penrose and W. Rindler, Spinors and space-time. Vol.2, Cambridge University Press (1984)
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Earlier work this paper cites.
V. Guillemin and S. Sternberg, “Geometric Quantization and Multiplicities of Group Representations,” Invent. Math 67
1990
Earlier work this paper cites.

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M. Kapovich and J. J. Millson, “The symplectic geometry of polygons in Euclidean space,” J. Differential Geom. 44
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M. Carfora, C. Dappiaggi and V. L. Gili, “Triangulated surfaces in twistor space: A kinematical set up for open/closed string duality,” JHEP 0612
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L. Freidel and S. Speziale, “Twisted geometries: A geometric parametrisation of SU(2) phase space,” arXiv:1001.2748 [gr-qc]
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C. Rovelli and S. Speziale, “On the geometry of loop quantum gravity on a graph,” arXiv:1005.2927 [gr-qc]
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B. Dittrich and J. P. Ryan, “Phase space descriptions for simplicial 4d geometries,” arXiv:0807.2806 [gr-qc]
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F. Conrady and L. Freidel, “Quantum geometry from phase space reduction,” arXiv:0902.0351 [gr-qc]
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L. Freidel, K. Krasnov and E. R. Livine, “Holomorphic Factorization for a Quantum Tetrahedron,” arXiv:0905.3627 [hep-th]
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Then

B. Dittrich and S. Speziale, “Area-angle variables for general relativity,” New J. Phys. 10
Original
2008
Later among the works it cites.
L. Freidel and E. R. Livine, “U(N) Coherent States for Loop Quantum Gravity,” arXiv:1005.2090 [gr-qc]
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2090
Closest in time.

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