Built on

J. Schwinger, “On Angular Momentum,” U.S. Atomic Energy Commission. (unpublished) NYO-3071, (1952)
1952
Earlier work this paper cites.
V. Bargmann, “On the Representations of the Rotation Group,” Rev. Mod. Phys. 34
1962
Earlier work this paper cites.
G. Ponzano; T. Regge, “Semiclassical limit of Racah coefficients”, p1-58, in: Spectroscopic and group theoretical methods in physics, ed. F. Bloch, North-Holland Publ. Co., Amsterdam, 1968
1968
Earlier work this paper cites.
J. J. Labarthe, “Generating Functions For The Coupling Recoupling Coefficients Of SU(2),” J. Phys. A 8
1975
Earlier work this paper cites.
B.W. Westbury, “A generating function for spin network evaluations, Knot theory,” Banach Center Publ. 42
1998
Earlier work this paper cites.
M. Mahajan and V. Vinay, Determinant: Old Algorithms, New Insights
1999
Earlier work this paper cites.
I. Kovacs and D.S. Silver and S.G. Williams, “Determinants of Commuting-block matrices,” Am. Math. Mon. 10
1999
Earlier work this paper cites.
Günter Rote, Division-Free Algorithms for the Determinant and the Pfaffian: Algebraic and Combinatorial Approaches
Original
2001
Earlier work this paper cites.

Similar

A. Ashtekar and J. Lewandowski, “Background independent quantum gravity: A Status report,” Class. Quant. Grav. 21
2004
Cited alongside, same era.
E. R. Livine and S. Speziale, “A New spinfoam vertex for quantum gravity,” Phys. Rev. D 76
Original
2007
Cited alongside, same era.
J. Engle, E. Livine, R. Pereira and C. Rovelli, LQG vertex with finite Immirzi parameter
Original
2008
Cited alongside, same era.
L. Freidel and K. Krasnov, A New Spin Foam Model for 4d Gravity
Original
2008
Cited alongside, same era.
F. Conrady and L. Freidel, “On the semiclassical limit of 4d spin foam models,” Phys. Rev. D 78
Original
2008

Then

J. W. Barrett and I. Naish-Guzm “The Ponzano-Regge model,” Class. Quant. Grav. 26
Original
2009
Later among the works it cites.
J. W. Barrett, W. J. Fairbairn and F. Hellmann, “Quantum gravity asymptotics from the SU(2) 15j symbol,” Int. J. Mod. Phys. A 25
Original
2010
Later among the works it cites.
L. Freidel and E. R. Livine, “The Fine Structure of SU(2) Intertwiners from U(N) Representations,” J. Math. Phys. 51
Original
2010
Later among the works it cites.
E. Bianchi, P. Dona and S. Speziale, “Polyhedra in loop quantum gravity,” Phys. Rev. D 83
Original
2011
Later among the works it cites.
M. Dupuis and E. R. Livine, “Holomorphic Simplicity Constraints for 4d Spinfoam Models,” Class. Quant. Grav. 28

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2012

On the exact evaluation of spin networks

Freidel, Laurent, Hnybida, Jeff

Understand

We introduce a fully coherent spin network amplitude whose expansion generates all SU(2) spin networks associated with a given graph.

We then give an explicit evaluation of this amplitude for an arbitrary graph.
We show how this coherent amplitude can be obtained from the specialization of a generating functional obtained by the contraction of parametrized intertwiners a la Schwinger.
We finally give the explicit evaluation of this generating functional for arbitrary graphs.

Built on

J. Schwinger, “On Angular Momentum,” U.S. Atomic Energy Commission. (unpublished) NYO-3071, (1952)
1952
Earlier work this paper cites.
V. Bargmann, “On the Representations of the Rotation Group,” Rev. Mod. Phys. 34
1962
Earlier work this paper cites.
G. Ponzano; T. Regge, “Semiclassical limit of Racah coefficients”, p1-58, in: Spectroscopic and group theoretical methods in physics, ed. F. Bloch, North-Holland Publ. Co., Amsterdam, 1968
1968
Earlier work this paper cites.
J. J. Labarthe, “Generating Functions For The Coupling Recoupling Coefficients Of SU(2),” J. Phys. A 8
1975
Earlier work this paper cites.
B.W. Westbury, “A generating function for spin network evaluations, Knot theory,” Banach Center Publ. 42
1998
Earlier work this paper cites.
M. Mahajan and V. Vinay, Determinant: Old Algorithms, New Insights
1999
Earlier work this paper cites.
I. Kovacs and D.S. Silver and S.G. Williams, “Determinants of Commuting-block matrices,” Am. Math. Mon. 10
1999
Earlier work this paper cites.
Günter Rote, Division-Free Algorithms for the Determinant and the Pfaffian: Algebraic and Combinatorial Approaches
Original
2001
Earlier work this paper cites.

Similar

A. Ashtekar and J. Lewandowski, “Background independent quantum gravity: A Status report,” Class. Quant. Grav. 21
2004
Cited alongside, same era.
E. R. Livine and S. Speziale, “A New spinfoam vertex for quantum gravity,” Phys. Rev. D 76
Original
2007
Cited alongside, same era.
J. Engle, E. Livine, R. Pereira and C. Rovelli, LQG vertex with finite Immirzi parameter
Original
2008
Cited alongside, same era.
L. Freidel and K. Krasnov, A New Spin Foam Model for 4d Gravity
Original
2008
Cited alongside, same era.
F. Conrady and L. Freidel, “On the semiclassical limit of 4d spin foam models,” Phys. Rev. D 78
Original
2008

Then

J. W. Barrett and I. Naish-Guzm “The Ponzano-Regge model,” Class. Quant. Grav. 26
Original
2009
Later among the works it cites.
J. W. Barrett, W. J. Fairbairn and F. Hellmann, “Quantum gravity asymptotics from the SU(2) 15j symbol,” Int. J. Mod. Phys. A 25
Original
2010
Later among the works it cites.
L. Freidel and E. R. Livine, “The Fine Structure of SU(2) Intertwiners from U(N) Representations,” J. Math. Phys. 51
Original
2010
Later among the works it cites.
E. Bianchi, P. Dona and S. Speziale, “Polyhedra in loop quantum gravity,” Phys. Rev. D 83
Original
2011
Later among the works it cites.
M. Dupuis and E. R. Livine, “Holomorphic Simplicity Constraints for 4d Spinfoam Models,” Class. Quant. Grav. 28

Beyond the bibliography

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

Open on alphaXiv

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Cited alongside, same era.

J. W. Barrett, R. J. Dowdall, W. J. Fairbairn, H. Gomes and F. Hellmann, “Asymptotic analysis of the EPRL four-simplex amplitude,” J. Math. Phys. 50

Original

2009

Cited alongside, same era.

F. Conrady and L. Freidel, “Quantum geometry from phase space reduction,” J. Math. Phys. 50

Original

2009

Cited alongside, same era.

S. Garoufalidis and R. Van der Veen, “Asymptotics of classical spin net-works,” arXiv:0902.3113 (2009)

Original

2009

Cited alongside, same era.

L. Freidel and S. Speziale, Twisted geometries: A geometric parametrisation of SU(2) phase space

Original

Cited in the paper.

M. Dupuis and E. R. Livine, “Holomorphic Simplicity Constraints for 4d Riemannian Spinfoam Models,” arXiv:1111.1125 [gr-qc]

Original

Cited in the paper.

R. Penrose, “Applications of negative dimensional tensors”, Advances in twistor theory, Huston and Ward eds. Research notes in mathematics, Pitman Publ. 308-312. R. Penrose, “Angular momentum: an approach to combinatorial space-time”, in Quantum theory and beyond, T. Bastin ed., Cambridge Univ. Press., New York, 151-180

Cited in the paper.

L. Freidel, K. Krasnov and E.R. Livine, Holomorphic Factorization for a Quantum Tetrahedron

Original

Cited in the paper.

Original

2011

Later among the works it cites.

F. Costantino and J. March«e “Generating series and asymptotics of classical spin networks,” arXiv:1103.5644 (2011)

Original

2011

Later among the works it cites.

L. Freidel and E. R. Livine, “U(N) Coherent States for Loop Quantum Gravity,” J. Math. Phys. 52

Original

2090

Closest in time.