Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space

Nuclear Physics B

Volumn 574, Issue 3, 2000, Pages 785-806

  De Pietri, Roberto ^a   Freidel, Laurent ^b   Krasnov, Kirill ^c   Rovelli, Carlo ^a,c,d  

^a Ctr de Phys Theor de Luminy   (France)

^b UNIVERSITÉ DE LYON   (France)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

Matrix models; Quantum gravity

Indexed keywords

EID: 0034701609     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(00)00005-5     Document Type: Article

References (58)

1. J.W. Barrett, L. Crane, J. Math. Phys. 39 (1998) 3296.
2. M.P. Reisenberger, C. Rovelli, Phys. Rev. D 56 (1997) 3490.
3. C. Rovelli, Nucl. Phys. B 57 (1997) 28.
4. C. Rovelli, gr-qc/9806121.
5. C. Rovelli, Loop quantum gravity, In: Living Reviews in Relativity, Electronic Journal, http://www.livingreviews.org, gr-qc/9710008.
6. J. Baez, Class. Quant. Grav. 15 (1998) 1827.
7. C. Rovelli, L. Smolin, Phys. Rev. D 52 (1995) 5743.
8. J. Baez, Adv. Math. 117 (1996) 253.
9. J. Baez, Strings, loops, knots and gauge fields, In: Knots and Quantum Gravity, ed. J. Baez, (Oxford Univ. Press, Oxford, 1994).
10. M. Reisenberger, World-sheet formulations of gauge theories and gravity, Talk given at the 7th Marcel Grossmann Meeting Stanford, July 1994, gr-qc/9412035.
11. J. Iwasaki, J. Math. Phys. 36 (1995) 6288.
12. J. Baez, An introduction to spin-foam models of BF theory and quantum gravity, to appear in to appear in geometry and quantum physics, ed. Helmut Gausterer and Harald Grosse, Lecture Notes in Physics (Springer, Berlin). xxx-archive:gr-qc/9905087.
13. M. Reisenberger, gr-qc/9711052.
14. F. Markopoulou, gr-qc/9704013.
15. F. Markopoulou, L. Smolin, Phys. Rev. D 58 (1998) 084032.
16. L. Smolin, hept-th/9001022,
17. L. Smolin, hep-th/9808192.
18. R. De Pietri, Canonical Loop Quantum Gravity and Spin-foam Models, to Appear in the Proc. of the XXIIIth Congress of the Italian Society for General Relativity and Gravitational Physics (SIGRAV), 1998, gr-qc/9903076.
19. J.W. Barrett, L. Crane, gr-qc/9904025.
20. J. Iwasaki, gr-qc/9903122.
21. J.W. Barrett, R. Williams, gr-qc/9809032.
22. F. David, Nucl. Phys. B 257 (1985) 45.
23. J. Ambjorn, B. Durhuus, J. Frolich, Nucl. Phys. B 257 (1985) 433.
24. V.A. Kazakov, I.K. Kostov, A.A. Migdal, Phys. Lett. 157 (1985) 295.
25. D.V. Boulatov, V.A. Kazakov, I.K. Kostov, A.A. Migdal, Nucl. Phys. B 275 (1986) 641.
26. M. Douglas, S. Shenker, Nucl. Phys. B 335 (1990) 635.
27. D. Gross, A. Migdal, Phys. Rev. Lett. 64 (1990) 635.
28. E. Brezin, V.A. Kazakov, Phys. Lett. B 236 (1990) 144.
29. D.V. Boulatov, Mod. Phys. Lett. A 7 (1992) 1629.
30. G. Ponzano, T. Regge, In: Spectroscopy and Group Theoretical Methods in Physics, ed. F. Bloch (North-Holland, Amsterdam, 1968).
31. V.G. Turaev, O.Y. Viro, Topology 31 (1992) 865.
32. V.G. Turaev, Quantum Invariants of Knots and 3-manifolds (de Gruyter, New York, 1994).
33. H. Ooguri, Mod. Phys. Lett. A 7 (1992) 2799.
34. L. Crane, D. Yetter, A categorical construction of 4D topological quantum field theories, in: Quantum Topology, ed. L. Kaufmann, R. Baadhio (World Scientific, Singapore, 1993), hep-th/9301062.
35. L. Crane, L. Kauffman, D. Yetter, J. Knot, Theor. Ramifications 6 (1997) 177. hep-th/9409167.
36. G. Horowitz, Comm. Math. Phys. 125 (1989) 417.
37. M. Blau, G. Thompson, Phys. Lett. B 228 (1989) 64.
38. J. Baez, Lett. Math. Phys. 38 (1996) 129.
39. R. De Pietri, L. Freidel, Class. Quant. Grav. 16 (1999) 2187, gr-qc/9804071.
40. M. Reisenberger, Class. Quant. Grav. 16 (1999) 1357, gr-qc/9804061.
41. A. Barbieri, Nucl. Phys. B 518 (1998) 714.
42. L. Freidel, K. Krasnov, Class. Quantum Grav. 16 (1999) 351.
43. J. Baez, J. Barrett, gr-qc/9903060.
44. L. Freidel, K. Krasnov, Adv. Theor. Math. Phys. 2 (1998) 1221.
45. L. Freidel, K. Krasnov, R. Puzio, hep-th/9901069.
46. L. Freidel, K. Krasnov, hep-th/9903192.
47. M.E. Peskin, D.V. Schroeder, An Introduction to Quantum Field Theory, (Addison Wesley, Reading, 1995).
48. R. Benedetti, C. Petronio, Manuscripta Mathematica 88 (1995) 291.
49. C. Petronio, Standard Spines and 3-Manifold, Collana Tesi di Perfezionamento, Scuola Normale Superiore, Pisa, 1995.
50. See also R. Benedetti, C. Petronio, Branched standard spine of 3-Manifolds, Lecture Notes in Mathematics N. 1653 (Springer, Berlin, 1997).
51. J. Ambjorn, M. Carfora, A. Marzuoli, The geometry of dynamical triangulations, Lecture Notes in Physics, (Springer, Berlin, 1997).
52. J. Ambjorn, M. Carfora, D. Gabrielli, A. Marzuoli, Nucl. Phys. B 542 (1999) 349.
53. R. De Pietri, Critical Behavior in the Convergence of Sums over Triangulations, unpublished.
54. M. Reisenberger, J. Math. Phys. 40 (1999) 2046.
55. C. Rovelli, L. Smolin, Nucl. Phys. B 442 (1995) 593.
56. C. Rovelli, L. Smolin, Nucl. Phys. B 456 (1995) 753, (E).
57. R. De Pietri, C. Rovelli, Phys. Rev. D 54 (1996) 2664.
58. N.J. Vilenkin, A.U. Klimyk, Representation of lie groups and special functions (Kluwer, Dordrecht, 1993), Vol. 2, Volume 2: Class I Representations, Special Functions, and Integral Transforms.