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The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where Lorentz covariance is manifest.
1915
Earlier work this paper cites.
F. Cianfrani and G. Montani, “Towards Loop Quantum Gravity without the time gauge,” Phys. Rev. Lett
1916
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C. Rovelli, “Simple model for quantum general relativity from loop quantum gravity,” arXiv:1010.1939
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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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S. Alexandrov, “Hilbert space structure of covariant loop quantum gravity,” Phys. Rev
2002
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S. Alexandrov and E. R. Livine, “SU(2) loop quantum gravity seen from covariant theory,” Phys. Rev
2003
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A. Ashtekar, M. Bojowald, and J. Lewandowski, “Mathematical structure of loop quantum cosmology,” Adv. Theor. Math. Phys
2003
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2007
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E. R. Livine and S. Speziale, “A new spinfoam vertex for quantum gravity,” Phys. Rev
2007
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S. Alexandrov, “Spin foam model from canonical quantization,” Phys. Rev
2008
Later among the works it cites.
S. Alexandrov, “Simplicity and closure constraints in spin foam models of gravity,” Phys. Rev
2008
Later among the works it cites.
2008
Later among the works it cites.
2010
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S. Alexandrov, “The new vertices and canonical quantization,” Phys. Rev
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2008
Cited alongside, same era.
2008
Cited alongside, same era.
L. Freidel and K. Krasnov, “A New Spin Foam Model for 4d Gravity,” Class. Quant. Grav
2008
Cited alongside, same era.
W. Wieland, “Complex Ashtekar variables and reality conditions for Holst’s action,” arXiv:1012.1738
Cited in the paper.
C. Rovelli, “A new look at loop quantum gravity,” arXiv:1004.1780
Cited in the paper.
C. Rovelli and M. Smerlak, “Spinfoams: summing = refining,” arXiv:1010.5437
Cited in the paper.
E. Magliaro and C. Perini, “Local spin foams,” arXiv:1010.5227
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2010
Closest in time.
M. Dupuis and E. R. Livine, “Lifting SU(2) Spin Networks to Projected Spin Networks,” Phys. Rev
2010
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2010
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