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E. R. Livine and S. Speziale, “Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity,” Europhys. Lett. 81
Original
1915
Earlier work this paper cites.
J. Schwinger, “On Angular Momentum,” U.S. Atomic Energy Commission. (unpublished) NYO-3071, (1952)
1952
Earlier work this paper cites.
T. Regge, “General Relativity Without Coordinates,” Nuovo Cim. 19
1961
Earlier work this paper cites.
V. Bargmann, “On the Representations of the Rotation Group,” Rev. Mod. Phys. 34
1962
Earlier work this paper cites.
J. F. Plebanski, “On the separation of Einsteinian substructures,” J. Math. Phys. 18
1977
Earlier work this paper cites.
U. Pachner, “P.L. homeomorphic manifolds are equivalent by elementary shellings,” European Journal of Combinatorics 12 (2), 129–145 (1991)
1991
Earlier work this paper cites.
I. Montvay and G. Münster, “Quantum fields on a lattice,” Cambridge, UK: Univ. Pr. (1994) 491 p. (Cambridge monographs on mathematical physics)
1994
Earlier work this paper cites.
A. Ashtekar and J. Lewandowski, “Projective techniques and functional integration for gauge theories,” J. Math. Phys. 36
1995
Earlier work this paper cites.
A. Ashtekar and J. Lewandowski, “Differential geometry on the space of connections via graphs and projective limits,” J. Geom. Phys. 17
1995
Earlier work this paper cites.
L. Freidel and K. Krasnov, Adv. Theor. Math. Phys. 2
1999
Earlier work this paper cites.
F. Markopoulou, “Coarse graining in spin foam models,” Class. Quant. Grav. 20
2003
Earlier work this paper cites.
R. Oeckl, “Renormalization of discrete models without background,” Nucl. Phys. B 657
2003
Earlier work this paper cites.
R. Oeckl, “Renormalization for spin foam models of quantum gravity,” In *Rio de Janeiro 2003, Recent developments in theoretical and experimental general relativity, gravitation, and relativistic field theories, pt. C* 2296-2300 [gr-qc/0401087]
2003
Earlier work this paper cites.
L. Freidel and D. Louapre, “Diffeomorphisms and spin foam models,” Nucl. Phys. B 662
2003
Earlier work this paper cites.
L. Freidel and E. R. Livine, “Spin networks for noncompact groups,” J. Math. Phys. 44
2003
Earlier work this paper cites.
J. Engle, R. Pereira and C. Rovelli, “The Loop-quantum-gravity vertex-amplitude,” Phys. Rev. Lett. 99
Original
2007
Earlier work this paper cites.
E.R. Livine and S. Speziale, “A new spinfoam vertex for quantum gravity”, Phys.Rev.D76 (2007) 084028 [arXiv:0705.0674]
Original
2007
Earlier work this paper cites.
M. Levin, C. P. Nave, “Tensor renormalization group approach to 2D classical lattice models,” Phys. Rev. Lett. 99
2007
Earlier work this paper cites.
E. R. Livine and D. Oriti, “Coupling of spacetime atoms and spin foam renormalisation from group field theory,” JHEP 0702
2007
Earlier work this paper cites.
L. Freidel and K. Krasnov, “A New Spin Foam Model for 4d Gravity,” Class. Quant. Grav. 25
Original
2008
Earlier work this paper cites.
J. Engle, R. Pereira and C. Rovelli, “Flipped spinfoam vertex and loop gravity,” Nucl. Phys. B 798
Original
2008
Earlier work this paper cites.

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J. Engle, E. Livine, R. Pereira and C. Rovelli, “LQG vertex with finite Immirzi parameter,” Nucl. Phys. B 799
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Then

S. Singh and G. Vidal, “Tensor network states and algorithms in the presence of a global SU(2) symmetry,” Phys. Rev. B 86
Original
2012
Later among the works it cites.
B. Dittrich, F. C. Eckert and M. Martin-Benito, “Coarse graining methods for spin net and spin foam models,” New J. Phys. 14
Original
2012
Later among the works it cites.
B. Dittrich and F. C. Eckert, “Towards computational insights into the large-scale structure of spin foams,” J. Phys. Conf. Ser. 360
Original
2012
Later among the works it cites.
B. Dittrich and S. Steinhaus, “Path integral measure and triangulation independence in discrete gravity,” Phys. Rev. D 85
Original
2012
Later among the works it cites.
M. X. Han and M. Zhang, “Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory,” Class. Quant. Grav. 29

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2014

Pachner moves in a 4d Riemannian holomorphic Spin Foam model

Banburski, Andrzej, Chen, Lin-Qing, Freidel, Laurent et al.

Understand

In this work we study a Spin Foam model for 4d Riemannian gravity, and propose a new way of imposing the simplicity constraints that uses the recently developed holomorphic representation.

Using the power of the holomorphic integration techniques, and with the introduction of two new tools: the homogeneity map and the loop identity, for the first time we give the analytic expressions for the behaviour of the Spin Foam amplitudes under 4-dimensional Pachner moves.
It turns out that this behaviour is controlled by an insertion of nonlocal mixing operators.
In the case of the 5-1 move, the expression governing the change of the amplitude can be interpreted as a vertex renormalisation equation.

Built on

E. R. Livine and S. Speziale, “Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity,” Europhys. Lett. 81
Original
1915
Earlier work this paper cites.
J. Schwinger, “On Angular Momentum,” U.S. Atomic Energy Commission. (unpublished) NYO-3071, (1952)
1952
Earlier work this paper cites.
T. Regge, “General Relativity Without Coordinates,” Nuovo Cim. 19
1961
Earlier work this paper cites.
V. Bargmann, “On the Representations of the Rotation Group,” Rev. Mod. Phys. 34
1962
Earlier work this paper cites.
J. F. Plebanski, “On the separation of Einsteinian substructures,” J. Math. Phys. 18
1977
Earlier work this paper cites.
U. Pachner, “P.L. homeomorphic manifolds are equivalent by elementary shellings,” European Journal of Combinatorics 12 (2), 129–145 (1991)
1991
Earlier work this paper cites.
I. Montvay and G. Münster, “Quantum fields on a lattice,” Cambridge, UK: Univ. Pr. (1994) 491 p. (Cambridge monographs on mathematical physics)
1994
Earlier work this paper cites.
A. Ashtekar and J. Lewandowski, “Projective techniques and functional integration for gauge theories,” J. Math. Phys. 36
1995
Earlier work this paper cites.
A. Ashtekar and J. Lewandowski, “Differential geometry on the space of connections via graphs and projective limits,” J. Geom. Phys. 17
1995
Earlier work this paper cites.
L. Freidel and K. Krasnov, Adv. Theor. Math. Phys. 2
1999
Earlier work this paper cites.
F. Markopoulou, “Coarse graining in spin foam models,” Class. Quant. Grav. 20
2003
Earlier work this paper cites.
R. Oeckl, “Renormalization of discrete models without background,” Nucl. Phys. B 657
2003
Earlier work this paper cites.
R. Oeckl, “Renormalization for spin foam models of quantum gravity,” In *Rio de Janeiro 2003, Recent developments in theoretical and experimental general relativity, gravitation, and relativistic field theories, pt. C* 2296-2300 [gr-qc/0401087]
2003
Earlier work this paper cites.
L. Freidel and D. Louapre, “Diffeomorphisms and spin foam models,” Nucl. Phys. B 662
2003
Earlier work this paper cites.
L. Freidel and E. R. Livine, “Spin networks for noncompact groups,” J. Math. Phys. 44
2003
Earlier work this paper cites.
J. Engle, R. Pereira and C. Rovelli, “The Loop-quantum-gravity vertex-amplitude,” Phys. Rev. Lett. 99
Original
2007
Earlier work this paper cites.
E.R. Livine and S. Speziale, “A new spinfoam vertex for quantum gravity”, Phys.Rev.D76 (2007) 084028 [arXiv:0705.0674]
Original
2007
Earlier work this paper cites.
M. Levin, C. P. Nave, “Tensor renormalization group approach to 2D classical lattice models,” Phys. Rev. Lett. 99
2007
Earlier work this paper cites.
E. R. Livine and D. Oriti, “Coupling of spacetime atoms and spin foam renormalisation from group field theory,” JHEP 0702
2007
Earlier work this paper cites.
L. Freidel and K. Krasnov, “A New Spin Foam Model for 4d Gravity,” Class. Quant. Grav. 25
Original
2008
Earlier work this paper cites.
J. Engle, R. Pereira and C. Rovelli, “Flipped spinfoam vertex and loop gravity,” Nucl. Phys. B 798
Original
2008
Earlier work this paper cites.