The physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory

Classical and Quantum Gravity

Volumn 27, Issue 20, 2010, Pages

  Ding, You ^a   Rovelli, Carlo ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78649618128     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/27/20/205003     Document Type: Article

References (54)

1. Reisenberger M P 1994 World sheet formulations of gauge theories and gravity arXiv:gr-qc/9412035
2. Iwasaki J 1996 Geometries induced by surfaces: an algorithm on the 3-dimensional simplex lattice Proc. 7th Marcel Grossmann Meeting on General Relativity (Stanford, 1994) ed R T Jantzen, GMKeiser and R Ruffini (River Edge, NJ: World Scientific) pp 803-4
3. Reisenberger M P and Rovelli C 1997 'Sum over surfaces' form of loop quantum gravity Phys. Rev. D 56 3490 (arXiv:gr-qc/9612035)
4. Baez J C 1998 Spin foam models Class. Quantum Grav. 15 1827-58 (arXiv:gr-qc/9709052)
5. Reisenberger M P and Rovelli C 2003 Spin foams as Feynman diagrams Florence 2001: A Relativistic Spacetime Odyssey ed I Ciufolini, D Dominici and L Lusanna (Singapore: World Scientific) pp 431-48 (arXiv:gr-qc/0002083)
6. Baez J C 2000 An introduction to spin foam models of BF theory and quantum gravity Lect. Notes Phys. 543 25-94
7. Reisenberger M P and Rovelli C 2001 Spacetime as a Feynman diagram: the connection formulation Class. Quantum Grav. 18 121-40
8. Reisenberger M P 1997 A lattice worldsheet sum for 4-d Euclidean general relativity arXiv:gr-qc/9711052
9. Barrett J W and Crane L 1998 Relativistic spin networks and quantum gravity J. Math. Phys. 39 3296-302
10. Barrett J W and Crane L 2000 A Lorentzian signature model for quantum general relativity Class. Quantum Grav. 17 3101-18
11. 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
12. Perez A and Rovelli C 2001 A spinfoam model without bubble divergences Nucl. Phys. B 599 255-82
13. 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
14. Oriti D 2001 Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity Rep. Prog. Phys. 64 1703-57
15. Perez A 2003 Spin foam models for quantum gravity Class. Quantum Grav. 20 R43
16. Ashtekar A and Lewandowski J 2004 Background independent quantum gravity: a status report Class. Quantum Grav. 21 R53-152
17. Ashtekar A 2007 An introduction to loop quantum gravity through cosmology Nuovo Cimento B 122 135 (arXiv:gr-qc/0702030)
18. Smolin L 2004 An invitation to loop quantum gravity arXiv:hep-th/0408048
19. Thiemann T 2004 Introduction to Modern Canonical Quantum General Relativity (Cambridge: Cambridge University Press) (arXiv:gr-qc/0110034)
20. Han M, HuangWand Ma Y 2007 Fundamental structure of loop quantum gravity Int. J. Mod. Phys. D 16 1397 (arXiv:gr-qc/0509064)
21. Rovelli C 2004 Quantum Gravity (Cambridge: Cambridge University Press)
22. Rovelli C and Smolin L 1988 Knot theory and quantum gravity Phys. Rev. Lett. 61 1155-8
23. RovelliCand Smolin L 1990 Loop space representation for quantum general relativity Nucl. Phys.B 331 80-152
24. Ashtekar A, Rovelli C and Smolin L 1992 Weaving a classical geometry with quantum threads Phys. Rev. Lett. 69 237
25. Rovelli C 2010 A new look at loop quantum gravity arXiv:1004.1780 [gr-qc]
26. Noui K and Perez A 2005 Three dimensional loop quantum gravity: physical scalar product and spin foam models Class. Quantum Grav. 22 1739 (arXiv:gr-qc/0402110)
27. Ashtekar A, Campiglia M and Henderson A 2009 Loop quantum cosmology and spin foams Phys. Lett. B 681 347-52 (arXiv:0909.4221 [gr-qc])
28. Ashtekar A, Campiglia M and Henderson A 2010 Casting loop quantum cosmology in the spin foam paradigm arXiv:1001.5147 [gr-qc]
29. Battisti M V, Marciano A and Rovelli C 2009 Triangulated loop quantum cosmology: Bianchi IX and inhomogenous perturbations arXiv:0911.2653 [gr-qc]
30. Rovelli C and Vidotto F 2009 On the spinfoam expansion in cosmology arXiv:0911.3097 [gr-qc]
31. Bianchi E, Rovelli C and Vidotto F 2010 Towards spinfoam cosmology arXiv:1003.3483 [gr-qc]
32. Engle J, Pereira R and Rovelli C 2007 The loop-quantum-gravity vertex-amplitude Phys. Rev. Lett. 99 161301 (arXiv:0705.2388 [gr-qc])
33. Engle J, Pereira R and Rovelli C 2008 Flipped spinfoam vertex and loop gravity Nucl. Phys. B 798 251-90 (arXiv:0708.1236 [gr-qc])
34. 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 [gr-qc])
35. Pereira R 2008 Lorentzian LQG vertex amplitude Class. Quantum Grav. 25 085013 (arXiv:0710.5043 [gr-qc])
36. Livine E and Speziale S 2007 A new spinfoam vertex for quantum gravity Phys. Rev. D 76 084028 (arXiv:0705.0674 [gr-qc])
37. Freidel L and Krasnov K 2008 A new spin foam model for 4d gravity Class. Quantum Grav. 25 125018 (arXiv:0708.1595 [gr-qc])
38. Livine E and Speziale S 2008 Consistently solving the simplicity constraints for spinfoam quantum gravity Europhys. Lett. 81 50004 (arXiv:0708.1915 [gr-qc])
39. 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 [gr-qc])
40. Ding Y and Rovelli C 2009 The volume operator in covariant quantum gravity arXiv:0911.0543 [gr-qc]
41. Bianchi E, Regoli D and Rovelli C 2010 Face amplitude of spinfoam quantum gravity arXiv:1005.0764 [gr-qc]
42. Ruhl W 1970 The Lorentz Group and Harmonic Analysis (New York: Benjamin)
43. Gel'fand I M, Graev M I and Vilenkin N Ya 1966 Generalized Functions: Volume 5. Integral Geometry and Representation Theory (New York: Academic)
44. Gel'fand I M, Minlos R A and Shapiro Z Ya 1963 Representations of the Rotation and Lorentzi Groups and Their Applications (Oxford: Pergamon) pp 187-9
45. Regge T 1961 General relativity without coordinates Nuovo Cimento 19 558-71
46. Livine E R 2002 Projected spin networks for Lorentz connection: linking spin foams and loop gravity Class. Quantum Grav. 19 5525
47. Kaminski W, Kisielowski M and Lewandowski J The EPRL intertwiners and corrected partition function arXiv:0912.0540 [gr-qc]
48. Rovelli C and Smolin L 1995 Discreteness of area and volume in quantum gravity Nucl. Phys. B 442 593-619
49. Rovelli C and Smolin L 1995 Nucl. Phys. B 456 734
50. Ashtekar A and Lewandowski J 1997 Quantum theory of geometry: I. Area operators Class. Quantum Grav. 14 A55-82
51. Ashtekar A and Lewandowski J 1997 Quantum theory of geometry: II. Volume operators Adv. Theor. Math. Phys. 1 388-429
52. Flori C and Thiemann T 2008 Semiclassical analysis of the loop quantum gravity volume operator: I. Flux coherent states arXiv:0812.1537 [gr-qc]
53. Flori C 2009 Semiclassical analysis of the loop quantum gravity volume operator: area coherent states arXiv:0904.1303 [gr-qc]
54. Alexandrov S 2010 The new vertices and canonical quantization arXiv:1004.2260 [gr-qc]