Twisted geometries: A geometric parametrisation of SU(2) phase space

@article{Freidel2010TwistedGA,
  title={Twisted geometries: A geometric parametrisation of SU(2) phase space},
  author={Laurent Freidel and Simone Speziale},
  journal={Physical Review D},
  year={2010},
  volume={82},
  pages={084040}
}
A cornerstone of the loop quantum gravity program is the fact that the phase space of general relativity on a fixed graph can be described by a product of SU(2) cotangent bundles per edge. In this paper we show how to parametrize this phase space in terms of quantities describing the intrinsic and extrinsic geometry of the triangulation dual to the graph. These are defined by the assignment to each face of its area, the two unit normals as seen from the two polyhedra sharing it, and an… 
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