Twisted geometries: A geometric parametrization of SU(2) phase space

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 82, Issue 8, 2010, Pages

  Freidel, Laurent ^a   Speziale, Simone ^b  

^a PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

^b CENTRE DE PHYSIQUE THÉORIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78651074923     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.82.084040     Document Type: Article

References (48)

1. A. Ashtekar, C. Rovelli, and L. Smolin, Phys. Rev. Lett. 69, 237 (1992). PRLTAO 0031-9007 10.1103/PhysRevLett.69.237
2. T. Thiemann, Classical Quantum Gravity CQGRDG 0264-9381 18, 2025 (2001); 10.1088/0264-9381/18/11/304
3. T. Thiemann Classical Quantum Gravity CQGRDG 0264-9381 23, 2063 (2006). 10.1088/0264-9381/23/6/013 (Pubitemid 43346572)
4. B. Bahr and T. Thiemann, Classical Quantum Gravity CQGRDG 0264-9381 26, 045011 (2009); 10.1088/0264-9381/26/4/045011
5. B. Bahr T. Thiemann Classical Quantum Gravity CQGRDG 0264-9381 26, 045012 (2009). 10.1088/0264-9381/26/4/045012
6. C. Flori and T. Thiemann, arXiv:0812.1537.
7. C. Rovelli, Phys. Rev. Lett. PRLTAO 0031-9007 97, 151301 (2006); 10.1103/PhysRevLett.97.151301 (Pubitemid 44547775)
8. 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
9. S. Speziale, Adv. Sci. Lett. 2, 280 (2009); 1936-6612
10. E. Alesci, E. Bianchi, and C. Rovelli, Classical Quantum Gravity CQGRDG 0264-9381 26, 215001 (2009). 10.1088/0264-9381/26/21/215001
11. E. Bianchi, E. Magliaro, and C. Perini, Nucl. Phys. NUPBBO 0550-3213 B822, 245 (2009). 10.1016/j.nuclphysb.2009.07.016
12. J. Engle, R. Pereira, and C. Rovelli, Phys. Rev. Lett. 99, 161301 (2007); PRLTAO 0031-9007 10.1103/PhysRevLett.99.161301 (Pubitemid 47587568)
13. J. Engle R. Pereira C. Rovelli Nucl. Phys. NUPBBO 0550-3213 B798, 251 (2008); 10.1016/j.nuclphysb.2008.02.002
14. R. Pereira, Classical Quantum Gravity CQGRDG 0264-9381 25, 085013 (2008); 10.1088/0264-9381/25/8/085013
15. J. Engle, E. Livine, R. Pereira, and C. Rovelli, Nucl. Phys. NUPBBO 0550-3213 B799, 136 (2008). 10.1016/j.nuclphysb.2008.02.018
16. E.R. Livine and S. Speziale, Phys. Rev. D PRVDAQ 1550-7998 76, 084028 (2007). 10.1103/PhysRevD.76.084028
17. E.R. Livine and S. Speziale, Europhys. Lett. 81, 50004 (2008). EULEEJ 0295-5075 10.1209/0295-5075/81/50004
18. L. Freidel and K. Krasnov, Classical Quantum Gravity CQGRDG 0264-9381 25, 125018 (2008). 10.1088/0264-9381/25/12/125018
19. F. Conrady and L. Freidel, Classical Quantum Gravity CQGRDG 0264-9381 25, 245010 (2008). 10.1088/0264-9381/25/24/245010
20. F. Conrady and L. Freidel, Phys. Rev. D PRVDAQ 1550-7998 78, 104023 (2008). 10.1103/PhysRevD.78.104023
21. F. Conrady and L. Freidel, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 50, 123510 (2009). 10.1063/1.3257109
22. 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
23. J.W. Barrett, R.J. Dowdall, W.J. Fairbairn, F. Hellmann, and R. Pereira, Classical Quantum Gravity CQGRDG 0264-9381 27, 165009 (2010). 10.1088/0264-9381/27/16/165009
24. L. Freidel and S. Speziale, " Quantum twisted geometries and coherent states " (unpublished).
25. E. Bianchi, E. Magliaro, and C. Perini, Phys. Rev. D PRVDAQ 1550-7998 82, 024012 (2010). 10.1103/PhysRevD.82.024012
26. A. Ashtekar and J. Lewandowski, Classical Quantum Gravity CQGRDG 0264-9381 21, R53 (2004); 10.1088/0264-9381/21/15/R01 (Pubitemid 39057347)
27. T. Thiemann, Modern Canonical Quantum General Relativity (Cambridge University Press, Cambridge, England, 2007), p. 819.
28. G. Immirzi, Classical Quantum Gravity CQGRDG 0264-9381 13, 2385 (1996); 10.1088/0264-9381/13/9/006 (Pubitemid 126118676)
29. G. Immirzi, Nucl. Phys. B, Proc. Suppl. NPBSE7 0920-5632 57, 65 (1997). 10.1016/S0920-5632(97)00354-X
30. B. Dittrich and J.P. Ryan, arXiv:0807.2806.
31. T. Regge, Nuovo Cimento NUCIAD 0029-6341 19, 558 (1961). 10.1007/BF02733251
32. L. Freidel and S. Speziale, " From twistors to twisted geometries " (unpublished).
33. C. Rovelli and S. Speziale, Classical Quantum Gravity CQGRDG 0264-9381 23, 5861 (2006). 10.1088/0264-9381/23/20/008 (Pubitemid 44460952)
34. L. Freidel, K. Krasnov, and E.R. Livine, Commun. Math. Phys. CMPHAY 0010-3616 297, 45 (2010). 10.1007/s00220-010-1036-5
35. L. Freidel and E.R. Livine, arXiv:0911.3553.
36. A. Barbieri, Nucl. Phys. NUPBBO 0550-3213 B518, 714 (1998). 10.1016/S0550-3213(98)00093-5
37. M. Kapovich and J.J. Millson, J. Diff. Geom. JDGEAS 0022-040X 44, 5861 (1996).
38. B. Dittrich and S. Speziale, New J. Phys. 10, 083006 (2008). NJOPFM 1367-2630 10.1088/1367-2630/10/8/083006
39. V. Bonzom, Phys. Rev. D PRVDAQ 1550-7998 80, 064028 (2009); 10.1103/PhysRevD.80.064028
40. see also V. Bonzom Classical Quantum Gravity CQGRDG 0264-9381 26, 155020 (2009). 10.1088/0264-9381/26/15/155020
41. Jean-Marie Souriau, Structure des Systèmes Dynamiques (Dunod, Paris, 1970).
42. N.M.J. Woodhouse, Geometric Quantization (Clarendon Press, Oxford, 1991).
43. V.I. Arnold, Mathematical Methods of Classical Mechanics (Springer, New York, 1997).
44. A.Y. Alekseev and A.Z. Malkin, Commun. Math. Phys. 162, 147 (1994). CMPHAY 0010-3616 10.1007/BF02105190
45. A. Ashtekar, A. Corichi, and J.A. Zapata, Classical Quantum Gravity CQGRDG 0264-9381 15, 2955 (1998). 10.1088/0264-9381/15/10/006 (Pubitemid 128140435)
46. E. Bianchi, Nucl. Phys. NUPBBO 0550-3213 B807, 591 (2009). 10.1016/j.nuclphysb.2008.08.013
47. B. Bahr and B. Dittrich, arXiv:0905.1670.
48. H. Waelbroeck and J.A. Zapata, Classical Quantum Gravity CQGRDG 0264-9381 11, 989 (1994). 10.1088/0264-9381/11/4/015