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arXiv · 1403.7482

Deformed Spinor Networks for Loop Gravity: Towards Hyperbolic Twisted Geometries

Maité Dupuis·Florian Girelli·Etera R. Livine
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Abstract

In the context of a canonical quantization of general relativity, one can deform the loop gravity phase space on a graph by replacing the T*SU(2) phase space attached to each edge by SL(2,C) seen as a phase space. This deformation is supposed to encode the presence of a non-zero cosmological constant. Here we show how to parametrize this phase space in terms of spinor variables, thus obtaining deformed spinor networks for loop gravity, with a deformed action of the gauge group SU(2) at the vertices. These are to be formally interpreted as the generalization of loop gravity twisted geometries to a hyperbolic curvature.

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Maité Dupuis, Florian Girelli, Etera R. Livine. 2014-03-28. Deformed Spinor Networks for Loop Gravity: Towards Hyperbolic Twisted Geometries. https://doi.org/10.1007/s10714-014-1802-3

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