Built on

S. Alexandrov, M. Geiller, and K. Noui, “Spin Foams and Canonical Quantization,” SIGMA 8
Original
1961
Earlier work this paper cites.
K. Schulten and R. G. Gordon, “Exact Recursive Evaluation of 3J and 6J Coefficients for Quantum Mechanical Coupling of Angular Momenta,” J. Math. Phys. 16
1970
Earlier work this paper cites.
K. Schulten and R. G. Gordon, “Semiclassical Approximation to 3j and 6j Coefficients for Quantum Mechanical Coupling of Angular Momenta,” J. Math. Phys. 16
1988
Earlier work this paper cites.
V. G. Turaev and O. Y. Viro, “State sum invariants of 3 manifolds and quantum 6j symbols,” Topology 31
1992
Earlier work this paper cites.
L. Freidel and K. Krasnov, “Discrete space-time volume for three-dimensional BF theory and quantum gravity,” Class. Quant. Grav. 16
1999
Earlier work this paper cites.
J. Roberts, “Asymptotics and 6j-symbols,” Geom. Topol. Monogr. 4
2002
Earlier work this paper cites.
L. Freidel and D. Louapre, “Asymptotics of 6j and 10j symbols,” Class. Quant. Grav. 20
2003
Earlier work this paper cites.
E. R. Livine and R. Oeckl, “Three-dimensional Quantum Supergravityand Supersymmetric Spin Foam Models,” Adv. Theor. Math. Phys. 7
2003
Earlier work this paper cites.
L. Freidel and D. Louapre, “Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles,” Class. Quant. Grav. 21
2004
Earlier work this paper cites.

Similar

K. Noui and A. Perez, “Three-dimensional loop quantum gravity: Physical scalar product and spin foam models,” Class. Quant. Grav. 22
2005
Cited alongside, same era.
J. Hackett and S. Speziale, “Grasping rules and semiclassical limit of the geometry in the Ponzano-Regge model,” Class. Quant. Grav. 24
2007
Cited alongside, same era.
R. Gurau, “The Ponzano-Regge asymptotic of the 6j symbol: An Elementary proof,” Annales Henri Poincare 9
Original
2008
Cited alongside, same era.
J. W. Barrett and I. Naish-Guzman, “The Ponzano-Regge model,” Class. Quant. Grav. 26
Original
2009
Cited alongside, same era.
PhD thesis, Lyon, IPN, 2010
Original
E. R. Livine, The Spinfoam Framework for Quantum Gravity · 2010

Then

V. Bonzom and M. Smerlak, “Bubble divergences from twisted cohomology,” Commun. Math. Phys. 312
Original
2012
Later among the works it cites.
V. Bonzom and M. Smerlak, “Gauge symmetries in spinfoam gravity: the case for ’cellular quantization’,” Phys. Rev. Lett. 108
Original
2012
Later among the works it cites.
M. Dupuis and F. Girelli, “Quantum hyperbolic geometry in loop quantum gravity with cosmological constant,” Phys. Rev. D87
Original
2013
Later among the works it cites.
D. Pranzetti, “Turaev-Viro amplitudes from 2+1 Loop Quantum Gravity,” Phys. Rev. D89
Original
2014
Later among the works it cites.
M. Dupuis and F. Girelli, “Observables in Loop Quantum Gravity with a cosmological constant,” Phys. Rev. D90

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2016

3d Quantum Gravity: Coarse-Graining and q-Deformation

Livine, Etera R.

Understand

The Ponzano-Regge state-sum model provides a quantization of 3d gravity as a spin foam, providing a quantum amplitude to each 3d triangulation defined in terms of the 6j-symbol (from the spin-recoupling theory of SU(2) representations).

In this context, the invariance of the 6j-symbol under 4-1 Pachner moves, mathematically defined by the Biedenharn-Elliot identity, can be understood as the invariance of the Ponzano-Regge model under coarse-graining or equivalently as the invariance of the amplitudes under the Hamiltonian constraints.
Here we look at length and volume insertions in the Biedenharn-Elliot identity for the 6j-symbol, derived in some sense as higher derivatives of the original formula.
This gives the behavior of these geometrical observables under coarse-graining.

Built on

S. Alexandrov, M. Geiller, and K. Noui, “Spin Foams and Canonical Quantization,” SIGMA 8
Original
1961
Earlier work this paper cites.
K. Schulten and R. G. Gordon, “Exact Recursive Evaluation of 3J and 6J Coefficients for Quantum Mechanical Coupling of Angular Momenta,” J. Math. Phys. 16
1970
Earlier work this paper cites.
K. Schulten and R. G. Gordon, “Semiclassical Approximation to 3j and 6j Coefficients for Quantum Mechanical Coupling of Angular Momenta,” J. Math. Phys. 16
1988
Earlier work this paper cites.
V. G. Turaev and O. Y. Viro, “State sum invariants of 3 manifolds and quantum 6j symbols,” Topology 31
1992
Earlier work this paper cites.
L. Freidel and K. Krasnov, “Discrete space-time volume for three-dimensional BF theory and quantum gravity,” Class. Quant. Grav. 16
1999
Earlier work this paper cites.
J. Roberts, “Asymptotics and 6j-symbols,” Geom. Topol. Monogr. 4
2002
Earlier work this paper cites.
L. Freidel and D. Louapre, “Asymptotics of 6j and 10j symbols,” Class. Quant. Grav. 20
2003
Earlier work this paper cites.
E. R. Livine and R. Oeckl, “Three-dimensional Quantum Supergravityand Supersymmetric Spin Foam Models,” Adv. Theor. Math. Phys. 7
2003
Earlier work this paper cites.
L. Freidel and D. Louapre, “Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles,” Class. Quant. Grav. 21
2004
Earlier work this paper cites.

Similar

K. Noui and A. Perez, “Three-dimensional loop quantum gravity: Physical scalar product and spin foam models,” Class. Quant. Grav. 22
2005
Cited alongside, same era.
J. Hackett and S. Speziale, “Grasping rules and semiclassical limit of the geometry in the Ponzano-Regge model,” Class. Quant. Grav. 24
2007
Cited alongside, same era.
R. Gurau, “The Ponzano-Regge asymptotic of the 6j symbol: An Elementary proof,” Annales Henri Poincare 9
Original
2008
Cited alongside, same era.
J. W. Barrett and I. Naish-Guzman, “The Ponzano-Regge model,” Class. Quant. Grav. 26
Original
2009
Cited alongside, same era.
PhD thesis, Lyon, IPN, 2010
Original
E. R. Livine, The Spinfoam Framework for Quantum Gravity · 2010