Coherent states, constraint classes and area operators in the new spin-foam models

Classical and Quantum Gravity

Volumn 25, Issue 10, 2008, Pages

  Engle, Jonathan ^a   Pereira, Roberto ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 44449086314     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/25/10/105010     Document Type: Article

References (37)

1. Rovelli C 2004 Quantum Gravity (Cambridge: Cambridge University Press)
2. Ashtekar A and Lewandowski J 2004 Background independent quantum gravity: a status report Class. Quantum Grav. 20 R53-152
3. Thiemann T 2007 Modern Canonical Quantum General Relativity (Cambridge: Cambridge University Press)
4. Thiemann T 1998 Quantum spin dynamics (QSD) Class. Quantum Grav. 15 839-73
5. Thiemann T 2006 Quantum spin dynamics: VIII. The master constraint Class. Quantum Grav. 23 2249-65
6. Perez A 2003 Spin foam models for quantum gravity Class. Quantum Grav. 20 R43
7. Oriti D 2001 Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity Rep. Prog. Phys. 64 1489-544
8. Barrett J W and Crane L 1998 Relativistic spin networks and quantum gravity J. Math. Phys. 39 3296-302
9. DePietri R, Freidel L, Krasnov K and Rovelli C 2000 Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space Nucl. Phys. B 574 785-806
10. Perez A and Rovelli C 2001 A spinfoam model without bubble divergences Nucl. Phys. B 599 255-82
11. Oriti D and Williams R M 2001 Gluing 4-simplices: a derivation of the Barrett-Crane spinfoam model for Euclidean quantum gravity Phys. Rev. D 63 024022
12. Alesci E and Rovelli C 2007 The full LQG graviton propagator: I. Difficulties with the Barrett-Crane vertex Phys. Rev. D 76 104012
13. Engle J, Pereira R and Rovelli C 2007 Loop-quantum-gravity vertex-amplitude Phys. Rev. Lett. 99 161301
14. Engle J, Pereira R and Rovelli C 2008 Flipped spinfoam vertex and loop gravity Nucl. Phys. B 798 251-90
15. Livine E and Speziale S 2007 A new spinfoam vertex for quantum gravity Phys. Rev. D 76 084028
16. Freidel L and Krasnov K 2007 A new spin foam model for 4d gravity Preprint 0708.1595
17. Livine E and Speziale S 2007 Consistently solving the simplicity constraints for spinfoam quantum gravity Preprint 0708.1915
18. Engle J, Livine E, Pereira R and Rovelli C 2007 LQG vertex with finite Immirzi parameter Preprint 0711.0146
19. Thiemann T 2006 The Phoenix project: master constraint programme for loop quantum gravity Class. Quantum Grav. 23 4453-72
20. Dittrich B and Thiemann T 2006 Testing the master constraint programme for loop quantum gravity: I. General framework Class. Quantum Grav. 23 1025-66
21. Dittrich B and Thiemann T 2006 Testing the master constraint programme for loop quantum gravity: II. Finite dimensional systems Class. Quantum Grav. 23 1067-88
22. Dittrich B and Thiemann T 2006 Testing the master constraint programme for loop quantum gravity: III. SL(2,R) models Class. Quantum Grav. 23 1089-120
23. Holst S 1996 Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action Phys. Rev. D 53 5966-9
24. Livine E and Oriti D 2002 Barrett-Crane spin foam model from generalized BF type action for gravity Phys. Rev. D 65 044025
25. Livine E 2002 Projected spin networks for Lorentz connection: linking spin foams and loop gravity Class. Quantum Grav. 19 5525-42
26. Reisenberger M 1999 On relativistic spin network vertices J. Math. Phys. 40 2046-54
27. Engle J 2006 Quantum field theory and its symmetry reduction Class. Quantum Grav. 23 2861-94
28. Ashtekar A and Tate R 1994 An algebraic extension of Dirac quantization: examples J. Math. Phys. 35 6434-70
29. Dirac P A M 1964 Lectures on Quantum Mechanics (New York: Yeshiva University)
30. Alexandrov S 2007 Spin foam model from canonical quantization Preprint 0705.3892
31. Rovelli C 2007 Comment on 'Are the spectra of geometrical operators in loop quantum gravity really discrete?' by B Dittrich and T Thiemann Preprint 0708.2481
32. Rovelli C 2002 Partial observables Phys. Rev. D 65 124013
33. Pereira R 2008 Lorentzian LQG vertex amplitude Class. Quantum. Grav. 25 085013
34. Perelomov A M 1986 Generalized Coherent States and Their Applications (Berlin: Springer)
35. Hartle J B and Sorkin R 1981 Boundary terms in the action for the Regge calculus Gen. Rel. Grav. 13 541-9
36. Ashtekar A, Bombelli L and Reula O 1991 'Covariant phase space of asymptotically flat gravitational fields' Mechanics, Analysis and Geometry: 200 Years after Lagrange ed M Francaviglia and D Holm (Amsterdam: North Holland)
37. Ashtekar A, Bombelli L and Koul R 1987 Phase space formulation of general relativity without 3+1 splitting The Physics of Phase Space ed Y S Kim and W W Zachary (Berlin: Springer)