690 citations · 5.8k across the 154 of their papers we have counts for
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gr-qc2013★ 44 cited
Deformation Operators of Spin Networks and Coarse-Graining
Etera R. Livine
In the context of loop quantum gravity, quantum states of geometry are mathematically defined as spin networks living on graphs embedded in the canonical space-like hypersurface. I…
math-ph2013★ 35 cited
Deformations of Polyhedra and Polygons by the Unitary Group
Etera R. Livine
We introduce the set of framed convex polyhedra with N faces as the symplectic quotient C^2N//SU(2). A framed polyhedron is then parametrized by N spinors living in C^2 satisfying…
gr-qc2013★ 31 cited
Holonomy Operator and Quantization Ambiguities on Spinor Space
Etera R. Livine, Johannes Tambornino
We construct the holonomy-flux operator algebra in the recently developed spinor formulation of loop gravity. We show that, when restricting to SU(2)-gauge invariant operators, the…