Built on

E. Livine, S. Speziale, “A New spinfoam vertex for quantum gravity”, arXiv:0705.0674. E. Livine, S. Speziale, “Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity”, arXiv:0708.1915
Original
1915
Earlier work this paper cites.
A.R. Edmonds, “Angular Momentum in Quantum Mechanics”, Princeton Univ. Press. (1957)
1957
Earlier work this paper cites.
J. F. Plebanski, “On the separation between Einsteinien substuctures”, J. Math. Phys. 12, 2511 (1977)
1977
Earlier work this paper cites.
C. Rovelli, L. Smolin, “Knot theory and quantum gravity” Phys Rev Lett
1995
Earlier work this paper cites.
A. Ashtekar, J. Lewandowski, “Projective techniques and functional integration” J. Math. Phys., 36:2170, 1995
1995
Earlier work this paper cites.
Anomaly-free formulation of non-perturbative, four-dimensional lorentzian quantum gravity
T. Thiemann · 1998
Earlier work this paper cites.
M. P. Reisenberger. “On Relativistic Spin Network Vertices” J.Math.Phys., 40:2046 2054, 1999. gr-qc/9809067
1999
Earlier work this paper cites.
A Perez, “Spin Foam Models for Quantum Gravity”, Class and Quantum Grav 20 (2003) R43 D. Oriti
M. P. Reisenberger and C. Rovelli. Sum over Surfaces form of Loop Quantum Gravity. Phys.Rev. D, 56:34903508, 1997. C. Rovelli. “The Projector on Physical States in Loop Quantum Gravity” Phys.Rev. D, 59:104015, 1999. J.C. Baez, “Spin foam models” Class Quant Grav · 2001
Earlier work this paper cites.

Similar

J. W. Barrett, L. Crane, “Relativistic spin networks and quantum gravity”, J. Math. Phys. 39 (1998) 3296–3302. R. De Pietri, L. Freidel, K. Krasnov, C. Rovelli, “Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space”, Nucl. Phys. B 574 (2000) 785. [arXiv:hep-th/9907154]. D. Oriti, R. M. Williams, “Gluing 4-simplices: a derivation of the Barrett-Crane spinfoam model for Euclidean quantum gravity”, Phys. Rev. D 63(2001) 024022. A. Perez, C. Rovelli, “A spin foam model without bubble divergences”, Nucl. Phys. B 599 (2001) 255
2001
Cited alongside, same era.
S. Alexandrov, E.Livine, “SU(2) loop quantum gravity seen from covariant theory”, Phys. Rev. D 67:044009, 2003
2003
Cited alongside, same era.
J. W. Barrett, R. M. Williams, “The asymptotics of an amplitude for the 4-simplex”, Adv. Theor. Math. Phys. 3 (1999) 209–215. J. C. Baez, J. D. Christensen, G. Egan, “Asymptotics of 10j symbols”, Class. Quant. Grav. 19 (2002) 6489. J. W. Barrett, C. M. Steele, “Asymptotics of relativistic spin networks”, Class. Quant. Grav. 20 (2003) 1341–1362. L. Freidel, D. Louapre, “Asymptotics of 6j and 10j symbols”, Class. Quant. Grav. 20 (2003) 1267–1294

Then

L. Freidel, K.Noui, P.Roche, “6J symbols duality relations”, J. Math. Phys. 48:113512, 2007
2007
Later among the works it cites.
E. Alesci, C.Rovelli, ”The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex ” Phys.Rev.D 76, 104012 (2007), arXiv:0708.0883 E. Alesci, C. Rovelli ”The complete LQG propagator: II. Asymptotic behavior of the vertex ” Phys.Rev.D 77, 044024 (2008) arXiv:0711.1284 E. Alesci, ”Tensorial Structure of the LQG graviton propagator” in Proceedings of the II Stueckelberg Workshop, Int.J.Mod.Phys.A 23:1209-1213, (2008), arXiv:0802.1201
Original
2008
Closest in time.
J. Engle, R. Pereira, C. Rovelli, “The loop-quantum-gravity vertex amplitude”, Phys. Rev. Lett., 99 (2007) 161301. J. Engle, R. Pereira, C. Rovelli, “Flipped spinfoam vertex and loop gravity”, Nucl.Phys.B798, 251-290 (2008), arXiv:0708.1236
Original
2008
Closest in time.
J. Engle, E. Livine, R. Pereira, C. Rovelli, “LQG vertex with finite Immirzi parameter”, Nucl.Phys.B799:136-149,2008 arXiv:0711.0146
Original
2008
Closest in time.

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2008

Spin-Foam Models and the Physical Scalar Product

Alesci, Emanuele, Noui, Karim, Sardelli, Francesco

Understand

This paper aims at clarifying the link between Loop Quantum Gravity and Spin-Foam models in four dimensions.

Starting from the canonical framework, we construct an operator P acting on the space of cylindrical functions Cyl($\Gamma$), where $\Gamma$ is the 4-simplex graph, such that its ma- trix elements are, up to some normalization factors, the vertex amplitude of Spin-Foam models.
The Spin-Foam models we are considering are the topological model, the Barrett-Crane model and the Engle-Pereira-Rovelli model.
The operator P is usually called the "projector" into physical states and its matrix elements gives the physical scalar product.

Built on

E. Livine, S. Speziale, “A New spinfoam vertex for quantum gravity”, arXiv:0705.0674. E. Livine, S. Speziale, “Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity”, arXiv:0708.1915
Original
1915
Earlier work this paper cites.
A.R. Edmonds, “Angular Momentum in Quantum Mechanics”, Princeton Univ. Press. (1957)
1957
Earlier work this paper cites.
J. F. Plebanski, “On the separation between Einsteinien substuctures”, J. Math. Phys. 12, 2511 (1977)
1977
Earlier work this paper cites.
C. Rovelli, L. Smolin, “Knot theory and quantum gravity” Phys Rev Lett
1995
Earlier work this paper cites.
A. Ashtekar, J. Lewandowski, “Projective techniques and functional integration” J. Math. Phys., 36:2170, 1995
1995
Earlier work this paper cites.
Anomaly-free formulation of non-perturbative, four-dimensional lorentzian quantum gravity
T. Thiemann · 1998
Earlier work this paper cites.
M. P. Reisenberger. “On Relativistic Spin Network Vertices” J.Math.Phys., 40:2046 2054, 1999. gr-qc/9809067
1999
Earlier work this paper cites.
A Perez, “Spin Foam Models for Quantum Gravity”, Class and Quantum Grav 20 (2003) R43 D. Oriti
M. P. Reisenberger and C. Rovelli. Sum over Surfaces form of Loop Quantum Gravity. Phys.Rev. D, 56:34903508, 1997. C. Rovelli. “The Projector on Physical States in Loop Quantum Gravity” Phys.Rev. D, 59:104015, 1999. J.C. Baez, “Spin foam models” Class Quant Grav · 2001
Earlier work this paper cites.

Similar

J. W. Barrett, L. Crane, “Relativistic spin networks and quantum gravity”, J. Math. Phys. 39 (1998) 3296–3302. R. De Pietri, L. Freidel, K. Krasnov, C. Rovelli, “Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space”, Nucl. Phys. B 574 (2000) 785. [arXiv:hep-th/9907154]. D. Oriti, R. M. Williams, “Gluing 4-simplices: a derivation of the Barrett-Crane spinfoam model for Euclidean quantum gravity”, Phys. Rev. D 63(2001) 024022. A. Perez, C. Rovelli, “A spin foam model without bubble divergences”, Nucl. Phys. B 599 (2001) 255
2001
Cited alongside, same era.
S. Alexandrov, E.Livine, “SU(2) loop quantum gravity seen from covariant theory”, Phys. Rev. D 67:044009, 2003
2003
Cited alongside, same era.
J. W. Barrett, R. M. Williams, “The asymptotics of an amplitude for the 4-simplex”, Adv. Theor. Math. Phys. 3 (1999) 209–215. J. C. Baez, J. D. Christensen, G. Egan, “Asymptotics of 10j symbols”, Class. Quant. Grav. 19 (2002) 6489. J. W. Barrett, C. M. Steele, “Asymptotics of relativistic spin networks”, Class. Quant. Grav. 20 (2003) 1341–1362. L. Freidel, D. Louapre, “Asymptotics of 6j and 10j symbols”, Class. Quant. Grav. 20 (2003) 1267–1294

Then

L. Freidel, K.Noui, P.Roche, “6J symbols duality relations”, J. Math. Phys. 48:113512, 2007
2007
Later among the works it cites.
E. Alesci, C.Rovelli, ”The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex ” Phys.Rev.D 76, 104012 (2007), arXiv:0708.0883 E. Alesci, C. Rovelli ”The complete LQG propagator: II. Asymptotic behavior of the vertex ” Phys.Rev.D 77, 044024 (2008) arXiv:0711.1284 E. Alesci, ”Tensorial Structure of the LQG graviton propagator” in Proceedings of the II Stueckelberg Workshop, Int.J.Mod.Phys.A 23:1209-1213, (2008), arXiv:0802.1201
Original
2008
Closest in time.
J. Engle, R. Pereira, C. Rovelli, “The loop-quantum-gravity vertex amplitude”, Phys. Rev. Lett., 99 (2007) 161301. J. Engle, R. Pereira, C. Rovelli, “Flipped spinfoam vertex and loop gravity”, Nucl.Phys.B798, 251-290 (2008), arXiv:0708.1236
Original
2008
Closest in time.
J. Engle, E. Livine, R. Pereira, C. Rovelli, “LQG vertex with finite Immirzi parameter”, Nucl.Phys.B799:136-149,2008 arXiv:0711.0146
Original
2008
Closest in time.

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

2003

Cited alongside, same era.

C. Rovelli, “Quantum Gravity”, (Cambridge University Press, Cambridge, 2004). T. Thiemann, “Modern canonical quantum general relativity”, (Cambridge University Press, Cambridge, UK, 2007). A. Ashtekar, J. Lewandowski, “Background independent quantum gravity: A status report”, Class. Quant. Grav. 21 (2004) R53

2004

Cited alongside, same era.

K. Noui, A. Perez, “Three Dimensional Loop Quantum Gravity: Spin-Foam models and the Physical Scalar Product”, Class. Quant. Grav. 22 (2005) 1739-1762, gr-qc/0402110

2005

Cited alongside, same era.

T. Thiemann, The Phoenix project: Master constraint programme for loop quantum gravity, Class. Quant. Grav., 23:2211-2248, 2006, gr-qc/0305080 B. Dittrich, T. Thiemann, Testing the master constraint programme for loop quantum gravity. I: General framework, Class. Quant. Grav., 23:1025-1066, 2006, grqc/ 0411138. T.Thiemann, Quantum spin dynamics. VIII: The master constraint, Class. Quant. Grav.,23:2249-2266, 2006, gr-qc/0510011;

2006

Cited alongside, same era.

L. Modesto, C. Rovelli, “Particle scattering in loop quantum gravity”, Phys. Rev. Lett. 95 (2005), 191301. C. Rovelli, “Graviton propagator from background–independent quantum gravity”, Phys. Rev. Lett. 97 (2006), 151301. E. Bianchi, L. Modesto, C. Rovelli, S. Speziale, “Graviton propagator in loop quantum gravity”, Class. Quant. Grav. 23 (2006), 6989-7028

2006

Cited alongside, same era.

J. C. Baez, J. D. Christensen, “Positivity of spin foam amplitudes,” Class. Quant. Grav. 19 (2002) 2291. J. D. Christensen, G. Egan, “An efficient algorithm for the Riemannian 10j symbols,” Class. Quant. Grav. 19 (2002) 1185. J. D. Christensen, “Finiteness of Lorentzian 10j symbols and partition functions,” Class. Quant. Grav. 23 (2006) 1679. I. Khavkine, J. D. Christensen, “q-Deformed spin foam models of quantum gravity”, Class. Quant. Grav. 24 (2007) 3271-3290

2007

Cited alongside, same era.

L. Freidel, K. Krasnov, “A New Spin Foam Model for 4d Gravity”, arXiv:0708.1595

Original

Cited in the paper.

F. Conrady, L. Freidel, “Path integral representation of spin foam models of 4d gravity” , arXiv:0806.4640

Original

Cited in the paper.

J.D. Christensen, E. Livine, S. Speziale, “Numerical evidence of regularized correlations in spin foam gravity”, arXiv:0710.0617

Original

Cited in the paper.

R. Pereira, “Lorentzian LQG vertex amplitude” , Class.Quant.Grav.25, 085013, (2008), arXiv:0710.5043