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We construct the holonomy-flux operator algebra in the recently developed spinor formulation of loop gravity.
1949
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T. Thiemann, Quantum Spin Dynamics (QSD)
1998
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J. Lewandowski and D. Marolf, Loop constraints: A habitat and their algebra
1998
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R. Gambini, J. Lewandowski, D. Marolf and J. Pullin, On the consistency of the constraint algebra in spin network quantum gravity
1998
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A. Barbieri, Quantum tetrahedra and simplicial spin networks
1998
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T. Thiemann, Closed formula for the matrix elements of the volume operator in canonical quantum gravity
1998
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F. Girelli and E.R. Livine, Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators
2005
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J. Brunnemann and T. Thiemann, Simplification of the Spectral Analysis of the Volume Operator in Loop Quantum Gravity
2006
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T. Thiemann, Modern canonical quantum general relativity
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J. Engle, E.R. Livine, R. Pereira and C. Rovelli, LQG vertex with finite Immirzi parameter
2008
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L. Freidel and S. Speziale, Twisted geometries: A geometric parametrisation of SU(2) phase space
2010
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L. Freidel and S. Speziale, From twistors to twisted geometries
2010
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L. Freidel and E.R. Livine, The Fine Structure of SU(2) Intertwiners from U(N) Representations
2010
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E.F. Borja, J. Diaz-Polo, I. Garay and E.R. Livine, Dynamics for a 2-vertex Quantum Gravity Model
2010
Cited alongside, same era.
M. Dupuis, S. Speziale and J. Tambornino, Spinors and Twistors in Loop Gravity and Spin Foams
M. Dupuis and E.R. Livine, Holomorphic Simplicity Constraints for 4d Riemannian Spinfoam Models
2011
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2011
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, V. Bonzom and L. Freidel, The Hamiltonian constraint in 3d Riemannian loop quantum gravity
2011
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E.R. Livine and J. Tambornino, Spinor Representation for Loop Quantum Gravity
2012
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2011
Cited alongside, same era.
2011
Cited alongside, same era.
E.R. Livine and J. Tambornino, Loop gravity in terms of spinors
2011
Cited alongside, same era.
M. Dupuis and E.R. Livine, Revisiting the Simplicity Constraints and Coherent Intertwiners
2011
Cited alongside, same era.
M. Dupuis and E.R. Livine, Holomorphic Simplicity Constraints for 4d Spinfoam Models
2011
Cited alongside, same era.
S. Speziale and W.M. Wieland, The twistorial structure of loop-gravity transition amplitudes
Cited in the paper.
W.M. Wieland, Hamiltonian spinfoam gravity
Cited in the paper.
L. Freidel and J. Hnybida, On the exact evaluation of spin networks
Cited in the paper.
2012
Later among the works it cites.
M. Dupuis, L. Freidel, E.R. Livine and S. Speziale, Holomorphic Lorentzian Simplicity Constraints
2012
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E.R. Livine, S. Speziale and J. Tambornino, Twistor Networks and Covariant Twisted Geometries
2012
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W.M. Wieland, Twistorial phase space for complex Ashtekar variables
2012
Later among the works it cites.