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2011

Twistor Networks and Covariant Twisted Geometries

Livine, Etera R., Speziale, Simone, Tambornino, Johannes

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We study the symplectic reduction of the phase space of two twistors to the cotangent bundle of the Lorentz group.

We provide expressions for the Lorentz generators and group elements in terms of the spinors defining the twistors.
We use this to define twistor networks as a graph carrying the phase space of two twistors on each edge.
We also introduce simple twistor networks, which provide a classical version of the simple projected spin networks living on the boundary Hilbert space of EPRL/FK spin foam models.

Twistor Networks and Covariant Twisted Geometries · Around

Built on

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E. R Livine, “Projected spin networks for Lorentz connection: Linking spin foams and loop gravity,” Class. Quant. Grav
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L. Freidel and E. R. Livine, Spin networks for noncompact groups J.Math.Phys.44 (2003) 1322-1356 [arXiv:hep-th/0205268]
2003
Earlier work this paper cites.
B. Dittrich, S. Speziale, Area-angle variables for general relativity, New J. Phys
Original
2008
Earlier work this paper cites.
C. Rovelli, S. Speziale, On the geometry of loop quantum gravity on a graph, Phys. Rev
Original
2010
Earlier work this paper cites.
L. Freidel and S. Speziale, Twisted geometries: A geometric parametrisation of SU(2) phase space, Phys.Rev.D82 (2010) 084040 [arXiv:1001.2748]
Original
2010
Earlier work this paper cites.
L. Freidel and S. Speziale, From twistors to twisted geometries, Phys.Rev.D82 (2010) 084041 [arXiv:1006.0199]
Original
2010
Earlier work this paper cites.

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