Lorentzian spin foam amplitudes: Graphical calculus and asymptotics

Classical and Quantum Gravity

Volumn 27, Issue 16, 2010, Pages

  Barrett, John W ^a   Dowdall, R J ^a   Fairbairn, Winston J ^a   Hellmann, Frank ^a   Pereira, Roberto ^b  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

^b CENTRE DE PHYSIQUE THÉORIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77954505264     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/27/16/165009     Document Type: Article

References (43)

1. Ponzano G and Regge T 1968 Semiclassical limit of Racah coefficients Spectroscopy and Group Theoretical Methods in Physics ed F Bloch (Amsterdam: North Holland) pp 1-58
2. Reisenberger M P and Rovelli C 1997 Sum over surfaces form of loop quantum gravity Phys. Rev. D 56 3490-508 (arXiv:gr-qc/9612035)
3. Ooguri H 1992 Topological lattice models in four-dimensions Mod. Phys. Lett. A 7 2799-810 (arXiv:hep-th/9205090)
4. Barrett J W and Crane L 1998 Relativistic spin networks and quantum gravity J. Math. Phys. 39 3296
5. Barrett J W and Crane L 2000 A Lorentzian signature model for quantum general relativity Class. Quantum Grav. 17 3101-18 (arXiv:gr-qc/9904025)
6. Engle J, Pereira R and Rovelli C 2008 Flipped spinfoam vertex and loop gravity Nucl. Phys. B 798 251-90 (arXiv:0708.1236)
7. Engle J, Livine E, Pereira R and Rovelli C 2008 LQG vertex with finite Immirzi parameter Nucl. Phys. B 799 136-49 (arXiv:0711.0146)
8. Freidel L and Krasnov K 2008 A new spin foam model for 4d gravity Class. Quantum Grav. 25 125018 (arXiv:0708.1595)
9. Livine E R and Speziale S 2008 Consistently solving the simplicity constraints for spinfoam quantum gravity Europhys. Lett. 81 50004 (arXiv:0708.1915)
10. Barbieri A 1998 Quantum tetrahedra and simplicial spin networks Nucl. Phys. B 518 714-28 (arXiv:gr-qc/9707010)
11. Pereira R 2008 Lorentzian LQG vertex amplitude Class. Quantum Grav. 25 085013 (arXiv:0710.5043)
12. Rovelli C 2004 Quantum Gravity (Cambridge: Cambridge University Press)
13. Alesci E and Rovelli C 2007 The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex Phys. Rev. D 76 104012 (arXiv:0708.0883)
14. Alesci E and Rovelli C 2008 The complete LQG propagator: II. Asymptotic behavior of the vertex Phys. Rev. D 77 044024 (arXiv:0711.1284)
15. Engle J, Pereira R and Rovelli C 2007 The loop-quantum-gravity vertex-amplitude Phys. Rev. Lett. 99 161301
16. Immirzi G 1997 Real and complex connections for canonical gravity Class. Quantum Grav. 14 L177-81 (arXiv:gr-qc/9612030)
17. Livine R E and Oriti D 2002 Barrett-Crane spin foam model from generalized BF-type action for gravity Phys. Rev. D 65 044025 (arXiv:gr-qc/0104043)
18. Engle J and Pereira R 2008 Coherent states, constraint classes, and area operators in the new spin-foam models Class. Quantum Grav. 25 105010 (arXiv:0710.5017)
19. Livine E R 2002 Projected spin networks for Lorentz connection: linking spin foams and loop gravity Class. Quantum Grav. 19 5525-42 (arXiv:gr-qc/ 0207084)
20. Reisenberger M 1999 On relativistic spin network vertices J. Math. Phys. 40 2046-54 (arXiv:gr-qc/9809067)
21. Barrett J W, Rocek M and Williams R M 1999 A note on area variables in Regge calculus Class. Quantum Grav. 16 1373-6 (arXiv:gr-qc/9710056)
22. Livine E R and Oriti D 2007 Coupling of spacetime atoms and spin foam renormalisation from group field theory J. High Energy Phys. JHEP02(2007)092 (arXiv:gr-qc/0512002)
23. Conrady F and Freidel L 2008 Path integral representation of spin foam models of 4d gravity Class. Quantum Grav. 25 245010 (arXiv:0806.4640)
24. Conrady F and Freidel L 2008 On the semiclassical limit of 4d spin foam models Phys. Rev. D 78 104023 (arXiv:0809.2280)
25. Barrett J W, Dowdall R J, Fairbairn W J, Gomes H and Hellmann F 2009 Asymptotic analysis of the EPRL four-simplex amplitude J. Math. Phys. 50 112504 (arXiv:0902.1170)
26. Bianchi E, Magliaro E and Perini C 2009 LQG propagator from the new spin foams Nucl. Phys. B 822 245-69 (arXiv:0905.4082)
27. Gelfand I, Graev M and Vilenkin N Y 1966 Generalized Functions: Vol 5. Integral Geometry and Representation Theory (New York: Academic)
28. Penrose R 1970 Angular momentum: an approach to combinatorial spacetime Quantum Theory and Beyond ed E T Bastin (Cambridge: Cambridge University Press)
29. Barrett J W and Naish-Guzman I 2009 The Ponzano-Regge model Class. Quantum Grav. 26 155014 (arXiv:0803.3319)
30. Reshetikhin N Y and Turaev V G 1990 Ribbon graphs and their invariants derived from quantum groups Commun. Math. Phys. 127 1-26
31. Alexandrov S 2008 Spin foam model from canonical quantization Phys. Rev. D 77 024009 (arXiv:0705.3892)
32. Baez J C and Barrett J W 2001 Integrability for relativistic spin networks Class. Quantum Grav. 18 4683-700 (arXiv:gr-qc/0101107)
33. Cherrington W J 2006 Finiteness and dual variables for Lorentzian spin foam models Class. Quantum Grav. 23 701
34. Christensen J D 2006 Finiteness of Lorentzian 10j symbols and partition functions Class. Quantum Grav. 23 1679
35. Engle J and Pereira R 2009 Regularization and finiteness of the Lorentzian LQG vertices Phys. Rev. D 79 084034 (arXiv:0805.4696)
36. Livine E R and Speziale S 2007 A new spinfoam vertex for quantum gravity Phys. Rev. D 76 084028
37. Perelomov A 1986 Generalized Coherent States and Their Applications (Berlin: Springer)
38. Naimark M A 1964 Linear Representations of the Lorentz Group (Oxford: Pergamon)
39. Ruhl W 1970 The Lorentz Group and Harmonic Analysis (New York: Benjamin)
40. Hormander L 1983 The Analysis of Linear Partial Differential Operators: I (Berlin: Springer)
41. Barrett J W, Fairbairn W J and Hellmann F 2010 Quantum gravity asymptotics from the su(2) 15j symbol Int. J. Mod. Phys. A 25 2897-2916 (arXiv:0912.4907)
42. Barrett J W and Foxon T J 1994 Semiclassical limits of simplicial quantum gravity Class. Quantum Grav. 11 543-56 (arXiv:gr-qc/9310016)
43. Dowdall R J, Gomes H and Hellmann F 2010 Asymptotic analysis of the Ponzano-Regge model for handlebodies J. Phys. A: Math. Theor. 43 115203 (arXiv:0909.2027)