Built on

P. Dona, M. Fanizza, G. Sarno and S. Speziale, Numerical study of the Lorentzian Engle-Pereira-Rovelli-Livine spin foam amplitude,
Original
1903
Earlier work this paper cites.
E. R. Livine and S. Speziale, Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
Original
1915
Earlier work this paper cites.
J. B. Hartle and R. Sorkin, Boundary Terms in the Action for the Regge Calculus
1981
Earlier work this paper cites.
Springer, 1986
A. M. Perelomov, Generalized coherent states and their applications · 1986
Earlier work this paper cites.
World Scientific, Singapore, 1988
D. A. Varshalovich, A. N. Moskalev and V. K. Khersonsky, Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3nj Symbols · 1988
Earlier work this paper cites.
K. Schulten and R. G. Gordon, Semiclassical approximations to 3j and 6j coefficients for quantum mechanical coupling of angular momenta
1988
Earlier work this paper cites.
H. Ooguri, Topological lattice models in four-dimensions
1992
Earlier work this paper cites.
M. Kapovich and J. Millson, The symplectic geometry of polygons in euclidean space
1996
Earlier work this paper cites.
J. W. Barrett and R. M. Williams, The Asymptotics of an amplitude for the four simplex
1999
Earlier work this paper cites.
S. Davids, Semiclassical limits of extended Racah coefficients
2000
Earlier work this paper cites.
J. D. Christensen and G. Egan, An Efficient algorithm for the Riemannian 10j symbols
2002
Earlier work this paper cites.
J. W. Barrett and C. M. Steele, Asymptotics of relativistic spin networks
2003
Earlier work this paper cites.
L. Freidel and D. Louapre, Diffeomorphisms and spin foam models
2003
Earlier work this paper cites.
Y. U. Taylor and C. T. Woodward, 6j symbols for and non-euclidean tetrahedra
2006
Earlier work this paper cites.
E. R. Livine and S. Speziale, A New spinfoam vertex for quantum gravity
Original
2007
Earlier work this paper cites.
J. Engle, R. Pereira and C. Rovelli, The Loop-quantum-gravity vertex-amplitude
Original
2007
Earlier work this paper cites.
P. Dona and S. Speziale, Asymptotics of lowest unitary SL(2,C) invariants on graphs
Original
2007
Earlier work this paper cites.
J. Engle, E. Livine, R. Pereira and C. Rovelli, LQG vertex with finite Immirzi parameter
Original
2008
Earlier work this paper cites.

Similar

L. Freidel and K. Krasnov, A New Spin Foam Model for 4d Gravity
Original
2008
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B. Dittrich and S. Speziale, Area-angle variables for general relativity
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2008
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V. Bonzom, E. R. Livine, M. Smerlak and S. Speziale, Towards the graviton from spinfoams: The Complete perturbative expansion of the 3d toy model
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J. W. Barrett, R. Dowdall, W. J. Fairbairn, H. Gomes and F. Hellmann, Asymptotic analysis of the EPRL four-simplex amplitude
Original

Then

Y. Ding, M. Han and C. Rovelli, Generalized Spinfoams
Original
2011
Later among the works it cites.
E. Bianchi, P. Dona and S. Speziale, Polyhedra in loop quantum gravity
Original
2011
Later among the works it cites.
V. Aquilanti, H. M. Haggard, A. Hedeman, N. Jeevanjee, R. G. Littlejohn and L. Yu, Semiclassical Mechanics of the Wigner 6 j 6j -Symbol
Original
2012
Later among the works it cites.
V. Bonzom and P. Fleury, Asymptotics of Wigner 3nj-symbols with Small and Large Angular Momenta: An Elementary Method
Original
2012
Later among the works it cites.
E. R. Livine and J. Tambornino, Spinor Representation for Loop Quantum Gravity
Original

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2017

SU(2) graph invariants, Regge actions and polytopes

Donà, Pietro, Fanizza, Marco, Sarno, Giorgio et al.

Understand

We revisit the the large spin asymptotics of 15j symbols in terms of cosines of the 4d Euclidean Regge action, as derived by Barrett and collaborators using a saddle point approximation.

We bring it closer to the perspective of area-angle Regge calculus and twisted geometries, and compute explicitly the Hessian and phase offsets.
We then extend it to more general SU(2) graph invariants, showing that saddle points still exist and have a similar structure.
For graphs dual to 4d polytopes we find again two distinct saddle points leading to a cosine asymptotic formula, however a conformal shape-mismatch is allowed by these configurations, and the asymptotic action is thus a generalisation of the Regge action.

Built on

P. Dona, M. Fanizza, G. Sarno and S. Speziale, Numerical study of the Lorentzian Engle-Pereira-Rovelli-Livine spin foam amplitude,
Original
1903
Earlier work this paper cites.
E. R. Livine and S. Speziale, Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
Original
1915
Earlier work this paper cites.
J. B. Hartle and R. Sorkin, Boundary Terms in the Action for the Regge Calculus
1981
Earlier work this paper cites.
Springer, 1986
A. M. Perelomov, Generalized coherent states and their applications · 1986
Earlier work this paper cites.
World Scientific, Singapore, 1988
D. A. Varshalovich, A. N. Moskalev and V. K. Khersonsky, Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3nj Symbols · 1988
Earlier work this paper cites.
K. Schulten and R. G. Gordon, Semiclassical approximations to 3j and 6j coefficients for quantum mechanical coupling of angular momenta
1988
Earlier work this paper cites.
H. Ooguri, Topological lattice models in four-dimensions
1992
Earlier work this paper cites.
M. Kapovich and J. Millson, The symplectic geometry of polygons in euclidean space
1996
Earlier work this paper cites.
J. W. Barrett and R. M. Williams, The Asymptotics of an amplitude for the four simplex
1999
Earlier work this paper cites.
S. Davids, Semiclassical limits of extended Racah coefficients
2000
Earlier work this paper cites.
J. D. Christensen and G. Egan, An Efficient algorithm for the Riemannian 10j symbols
2002
Earlier work this paper cites.
J. W. Barrett and C. M. Steele, Asymptotics of relativistic spin networks
2003
Earlier work this paper cites.
L. Freidel and D. Louapre, Diffeomorphisms and spin foam models
2003
Earlier work this paper cites.
Y. U. Taylor and C. T. Woodward, 6j symbols for and non-euclidean tetrahedra
2006
Earlier work this paper cites.
E. R. Livine and S. Speziale, A New spinfoam vertex for quantum gravity
Original
2007
Earlier work this paper cites.
J. Engle, R. Pereira and C. Rovelli, The Loop-quantum-gravity vertex-amplitude
Original
2007
Earlier work this paper cites.
P. Dona and S. Speziale, Asymptotics of lowest unitary SL(2,C) invariants on graphs
Original
2007
Earlier work this paper cites.
J. Engle, E. Livine, R. Pereira and C. Rovelli, LQG vertex with finite Immirzi parameter
Original
2008
Earlier work this paper cites.