Spinfoams in the holomorphic representation

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 82, Issue 12, 2010, Pages

  Bianchi, Eugenio ^a   Magliaro, Elena ^a   Perini, Claudio ^a,b  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

^b ROMA TRE UNIVERSITY   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78651289042     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.82.124031     Document Type: Article

References (74)

1. M.P. Reisenberger and C. Rovelli, Phys. Rev. D PRVDAQ 0556-2821 56, 3490 (1997). 10.1103/PhysRevD.56.3490
2. A. Perez, Classical Quantum Gravity 20, R43 (2003). CQGRDG 0264-9381 10.1088/0264-9381/20/6/202
3. C. Rovelli, Quantum Gravity (Cambridge University Press, Cambridge, England, 2004).
4. A. Ashtekar and J. Lewandowski, Classical Quantum Gravity 21, R53 (2004) 10.1088/0264-9381/21/15/R01. CQGRDG 0264-9381
5. T. Thiemann, Modern Canonical Quantum General Relativity (Cambridge University Press, Cambridge, England, 2007).
6. C. Rovelli, arXiv:1004.1780.
7. E.R. Livine and S. Speziale, Phys. Rev. D PRVDAQ 1550-7998 76, 084028 (2007). 10.1103/PhysRevD.76.084028
8. J. Engle, E. Livine, R. Pereira, and C. Rovelli, Nucl. Phys. B NUPBBO 0550-3213 799, 136 (2008). 10.1016/j.nuclphysb.2008.02.018
9. L. Freidel and K. Krasnov, Classical Quantum Gravity CQGRDG 0264-9381 25, 125018 (2008). 10.1088/0264-9381/25/12/125018
10. W. Kaminski, M. Kisielowski, and J. Lewandowski, Classical Quantum Gravity CQGRDG 0264-9381 27, 095006 (2010). 10.1088/0264-9381/27/9/095006
11. A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourao, and T. Thiemann, J. Funct. Anal. 135, 519 (1996). JFUAAW 0022-1236 10.1006/jfan.1996.0018 (Pubitemid 126166748)
12. T. Thiemann, Classical Quantum Gravity CQGRDG 0264-9381 18, 2025 (2001); 10.1088/0264-9381/18/11/304
13. T. Thiemann and O. Winkler, Classical Quantum Gravity CQGRDG 0264-9381 18, 2561 (2001); 10.1088/0264-9381/18/14/301
14. T. Thiemann O. Winkler Classical Quantum Gravity CQGRDG 0264-9381 18, 4629 (2001); 10.1088/0264-9381/18/21/315
15. T. Thiemann O. Winkler Classical Quantum Gravity CQGRDG 0264-9381 18, 4997 (2001). 10.1088/0264-9381/18/23/302
16. H. Sahlmann, T. Thiemann, and O. Winkler, Nucl. Phys. B NUPBBO 0550-3213 606, 401 (2001). 10.1016/S0550-3213(01)00226-7 (Pubitemid 33571176)
17. T. Thiemann, Classical Quantum Gravity CQGRDG 0264-9381 23, 2063 (2006). 10.1088/0264-9381/23/6/013 (Pubitemid 43346572)
18. B. Bahr and T. Thiemann, Classical Quantum Gravity 26, 045011 (2009); CQGRDG 0264-9381 10.1088/0264-9381/26/4/045011
19. B. Bahr T. Thiemann Classical Quantum Gravity 26, 045012 (2009). CQGRDG 0264-9381 10.1088/0264-9381/26/4/045012
20. E. Bianchi, E. Magliaro, and C. Perini, Phys. Rev. D PRVDAQ 1550-7998 82, 024012 (2010). 10.1103/PhysRevD.82.024012
21. J.W. Barrett, R.J. Dowdall, W.J. Fairbairn, H. Gomes, and F. Hellmann, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 50, 112504 (2009). 10.1063/1.3244218
22. J.W. Barrett, R.J. Dowdall, W.J. Fairbairn, F. Hellmann, and R. Pereira, Classical Quantum Gravity 27, 165009 (2010). CQGRDG 0264-9381 10.1088/0264-9381/27/16/165009
23. C.W. Misner, Rev. Mod. Phys. 29, 497 (1957). RMPHAT 0034-6861 10.1103/RevModPhys.29.497
24. S.W. Hawking, in General Relativity, an Einstein Centenary Survey (Cambridge University Press, Cambridge, England, 1979).
25. R. Oeckl, Phys. Lett. B 575, 318 (2003). PYLBAJ 0370-2693 10.1016/j.physletb.2003.08.043
26. D. Oriti, arXiv:0912.2441.
27. A. Perez and C. Rovelli, Nucl. Phys. B NUPBBO 0550-3213 599, 255 (2001). 10.1016/S0550-3213(01)00030-X (Pubitemid 33377093)
28. C. Perini, C. Rovelli, and S. Speziale, Phys. Lett. B 682, 78 (2009). PYLBAJ 0370-2693 10.1016/j.physletb.2009.10.076
29. L. Freidel, R. Gurau, and D. Oriti, Phys. Rev. D PRVDAQ 1550-7998 80, 044007 (2009). 10.1103/PhysRevD.80.044007
30. J. Magnen, K. Noui, V. Rivasseau, and M. Smerlak, Classical Quantum Gravity CQGRDG 0264-9381 26, 185012 (2009). 10.1088/0264-9381/26/18/185012
31. V. Bonzom and M. Smerlak, Lett. Math. Phys. 93, 295 (2010). LMPHDY 0377-9017 10.1007/s11005-010-0414-4
32. J.B. Geloun, T. Krajewski, J. Magnen, and V. Rivasseau, Classical Quantum Gravity CQGRDG 0264-9381 27, 155012 (2010). 10.1088/0264-9381/27/15/155012
33. J.B. Geloun, R. Gurau, and V. Rivasseau, arXiv:1008.0354.
34. T. Krajewski, J. Magnen, V. Rivasseau, A. Tanasa, and P. Vitale, arXiv:1007.3150.
35. C. Rovelli (private communication).
36. E. Bianchi, D. Regoli, and C. Rovelli, Classical Quantum Gravity 27, 185009 (2010). CQGRDG 0264-9381 10.1088/0264-9381/27/18/185009
37. G. Ponzano and T. Regge, in Spectroscopic and Group Theoretical Methods in Physics, edited by, Bloch, (North-Holland, Amsterdam, 1968).
38. F. Conrady and L. Freidel, Classical Quantum Gravity CQGRDG 0264-9381 25, 245010 (2008). 10.1088/0264-9381/25/24/245010
39. F. Conrady and L. Freidel, Phys. Rev. D PRVDAQ 1550-7998 78, 104023 (2008). 10.1103/PhysRevD.78.104023
40. R.J. Dowdall, H. Gomes, and F. Hellmann, J. Phys. A JPHAC5 1751-8113 43, 115203 (2010). 10.1088/1751-8113/43/11/115203
41. F. Conrady and L. Freidel, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 50, 123510 (2009); 10.1063/1.3257109
42. L. Freidel, K. Krasnov, and E.R. Livine, Commun. Math. Phys. 297, 45 (2010). CMPHAY 0010-3616 10.1007/s00220-010-1036-5
43. F. Bloch, Phys. Rev. 70, 460 (1946). PHRVAO 0031-899X 10.1103/PhysRev.70.460
44. B.C. Hall, J. Funct. Anal. 122, 103 (1994); JFUAAW 0022-1236 10.1006/jfan.1994.1064
45. B.C. Hall Commun. Math. Phys. CMPHAY 0010-3616 226, 233 (2002). 10.1007/s002200200607 (Pubitemid 36195043)
46. L. Freidel and S. Speziale, Phys. Rev. D PRVDAQ 1550-7998 82, 084040 (2010). 10.1103/PhysRevD.82.084040
47. V. Bonzom, Classical Quantum Gravity 26, 155020 (2009). CQGRDG 0264-9381 10.1088/0264-9381/26/15/155020
48. D. Oriti and T. Tlas, Classical Quantum Gravity 27, 135018 (2010). CQGRDG 0264-9381 10.1088/0264-9381/27/13/135018
49. B. Dittrich and J.P. Ryan, arXiv:0807.2806.
50. E. Bianchi, Nucl. Phys. B NUPBBO 0550-3213 807, 591 (2009). 10.1016/j.nuclphysb.2008.08.013
51. A. Baratin and D. Oriti, Phys. Rev. Lett. 105, 221302 (2010); PRLTAO 0031-9007 10.1103/PhysRevLett.105.221302
52. A. Baratin, B. Dittrich, D. Oriti, and J. Tambornino, arXiv:1004.3450.
53. T. Regge, Nuovo Cimento NUCIAD 0029-6341 19, 558 (1961). 10.1007/BF02733251
54. L. Modesto and C. Rovelli, Phys. Rev. Lett. 95, 191301 (2005); PRLTAO 0031-9007 10.1103/PhysRevLett.95.191301 (Pubitemid 41777188)
55. C. Rovelli, Phys. Rev. Lett. 97, 151301 (2006); PRLTAO 0031-9007 10.1103/PhysRevLett.97.151301 (Pubitemid 44547775)
56. E. Bianchi, L. Modesto, C. Rovelli, and S. Speziale, Classical Quantum Gravity CQGRDG 0264-9381 23, 6989 (2006); 10.1088/0264-9381/23/23/024
57. E. Alesci and C. Rovelli, Phys. Rev. D PRVDAQ 1550-7998 76, 104012 (2007); 10.1103/PhysRevD.76.104012
58. E. Alesci C. Rovelli Phys. Rev. D PRVDAQ 1550-7998 77, 044024 (2008); 10.1103/PhysRevD.77.044024
59. E. Alesci, E. Bianchi, and C. Rovelli, Classical Quantum Gravity 26, 215001 (2009); CQGRDG 0264-9381 10.1088/0264-9381/26/21/215001
60. S. Speziale, Adv. Sci. Lett. 2, 280 (2009); 1936-6612 arXiv:0810.1978v2
61. E. Bianchi, E. Magliaro, and C. Perini, Nucl. Phys. B NUPBBO 0550-3213 822, 245 (2009). 10.1016/j.nuclphysb.2009.07.016
62. E. Alesci, E. Bianchi, E. Magliaro, and C. Perini, Classical Quantum Gravity CQGRDG 0264-9381 27, 095016 (2010). 10.1088/0264-9381/27/9/095016
63. E. Magliaro, C. Perini, and C. Rovelli, Classical Quantum Gravity 25, 095009 (2008); CQGRDG 0264-9381 10.1088/0264-9381/25/9/095009
64. E. Alesci, E. Bianchi, E. Magliaro, and C. Perini, Classical Quantum Gravity 26, 185003 (2009); CQGRDG 0264-9381 10.1088/0264-9381/26/18/185003
65. I. Khavkine, Classical Quantum Gravity 26, 125012 (2009); CQGRDG 0264-9381 10.1088/0264-9381/26/12/125012
66. I. Khavkine, arXiv:0810.1653v2 [gr-qc].
67. R. Pereira, Classical Quantum Gravity 25, 085013 (2008). CQGRDG 0264-9381 10.1088/0264-9381/25/8/085013
68. J. Engle and R. Pereira, Phys. Rev. D PRVDAQ 1550-7998 79, 084034 (2009). 10.1103/PhysRevD.79.084034
69. W. Ruhl, The Lorentz Group and Harmonic Analysis (Benjamin, New York, 1970);
70. I. Gelfand, M. Graev, and N. Vilenkin, Generalized Functions Vol. 5: Integral Geometry and Representation Theory (Academic Press, 1966).
71. E.R. Livine, Classical Quantum Gravity CQGRDG 0264-9381 19, 5525 (2002). 10.1088/0264-9381/19/21/316 (Pubitemid 37026840)
72. R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill Companies, 1965).
73. E. Bianchi and A. Satz, Nucl. Phys. B NUPBBO 0550-3213 808, 546 (2009). 10.1016/j.nuclphysb.2008.09.005
74. E. Bianchi, C. Rovelli, and F. Vidotto, Phys. Rev. D PRVDAQ 1550-7998 82, 084035 (2010). 10.1103/PhysRevD.82.084035