Three-dimensional quantum supergravity and supersymmetric spin foam models

Advances in Theoretical and Mathematical Physics

Volumn 7, Issue 6, 2003, Pages 951-1001

  Livine, Etera R ^a   Oeckl, Robert ^a  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 14744291624     PISSN: 10950761     EISSN: 10950753     Source Type: Journal    
DOI: 10.4310/ATMP.2003.v7.n6.a2     Document Type: Article

References (46)

1. JC Baez, An Introduction to Spin Foam Models of Quantum Gravity and BF Theory, Lect.Notes Phys. 543 (2000) 25-94
2. D Oriti, Spacetime geometry from algebra: spin foam models for nonperturbative quantum gravity, Rept.Prog.Phys. 64 (2001) 1489-1544
3. A Perez, Spin Foam Models for Quantum Gravity, Class.Quant.Grav. 20 (2003) R43
4. R Oeckl, Generalized Lattice Gauge Theory, Spin Foams and State Sum Invariants, J.Geom.Phys. 46 (2003) 308-354
5. A Mikovic, Spin Foam Models of Matter Coupled to Gravity, Class.Quant.Grav. 19 (2002) 2335-2354
6. L Crane, A New Approach to the Geometrization of Matter
7. D Oriti, H Pfeiffer, A spin foam model for pure gauge theory coupled to quantum gravity, Phys.Rev. D66 (2002) 124010
8. A Mikovic, Spin Foam Models of Yang-Mills Theory Coupled to Gravity, Class.Quant.Grav. 20 (2003) 239-246
9. G Ponzano, T Regge, Semiclassical limit of Racah coefficients, Spectro-scopic and Group Theoretical Methods in Physics (ed. F. Bloch et al.), North-Holland, Amsterdam, 1968
10. H Ooguri, Partition Functions and Topology-Changing Amplitudes in the 3D Lattice Gravity of Ponzano and Regge, Nucl.Phys. B382 (1992) 276-304
11. A Achúcarro, PK Townsend, A Chern-Simons action for three-dimensional Anti-De Sitter supergravity theories, Phys.Lett. B180 (1986) 89.
12. A Achúcarro, PK Townsend, Extended Supergravities in d = 2 + 1 as Chern-Simons theories, Phys.Lett. B229 (1989) 383
13. JW Barrett, BW Westbury, Invariants of piecewise-linear 3-manifolds, Trans. Amer. Math. Soc. 348 (1996) 3997-4022.
14. L Crane, LH Kauffman, DN Yetter, State-Sum Invariants of 4-Manifolds, J. Knot Theory Ram. 6 (1997) 177-234
15. L Freidel, K Krasnov, Discrete Space-Time Volume for 3-Dimensional BF Theory and Quantum Gravity, Class.Quant.Grav. 16 (1999) 351-362.
16. L Freidel, K Krasnov, R Puzio, BF Description of Higher-Dimensional Gravity Theories, Adv.Theor.Math.Phys. 3 (1999) 1289-1324
17. JW Barrett, L Crane, Relativistic spin networks and quantum gravity, J.Math.Phys. 39 (1998) 3296-3302, gr-qc/9709028;
18. JW Barrett, L Crane, A Lorentzian Signature Model for Quantum General Relativity, Class.Quant.Grav. 17 (2000) 3101-3118
19. Y Ling, L Smolin, Eleven dimensional supergravity as a constrained topological field theory, Nucl.Phys. B601 (2001) 191-208
20. R Oeckl, Renormalisation of discrete models without background, Nucl.Phys. B657 (2003) 107-138
21. R Oeckl, The quantum geometry of spin and statistics, J.Geom.Phys. 39 (2001) 233-252
22. E Witten, (2 + 1)-Dimensional Gravity as an Exactly Soluble System, Nucl.Phys. B311 (1988) 46.
23. T Thiemann, QSD IV : 2 + 1 Euclidean Quantum Gravity as a model to test 3+1 Lorentzian Quantum Gravity, Class.Quant.Grav. 15 (1998) 1249-1280
24. L Freidel, ER Livine, C Rovelli, Spectra of Length and Area in 2+1 Lorentzian Loop Quantum Gravity, Class.Quant.Grav. 20 (2003) 1463-1478
25. F Girelli, R Oeckl, A Perez, Spin foam diagrammatics and topological invariance, Class.Quant.Grav. 19 (2002) 1093-1108
26. VG Turaev, OY Viro, State sum invariants of 3-manifolds and quantum 6j-symbols, Topology 31 (1992) 865-902
27. H Ooguri, Topological lattice models in four dimensions, Mod.Phys.Lett. A7 (1992) 2799-2810
28. R Oeckl, Braided Quantum Field Theory, Commun.Math.Phys. 217 (2001) 451-473
29. C Rovelli, Partial observables, Phys.Rev. D65 (2002) 124013
30. R Oeckl, The quantum geometry of supersymmetry and the generalized group extension problem, J.Geom.Phys. 44 (2002) 299-330
31. M Scheunert, W Nahm, V Rittenberg, Irreducible representations of the osp(2,1) and spl(2, 1) graded Lie algebras, J.Math.Phys. 18 (1977) 155.
32. P Minnaert, S Toshev, Racah Sum Rule and Biedenharn-Elliott Identity for the Super-Rotation 6-j symbols, J.Math.Phys. 35 (1994) 5057-5064
33. L Freidel, D Louapre, Diffeomorphisms and spin foam models, Nucl.Phys. B662 (2003) 279-298
34. JC Baez, Spin foam models, Class. Quantum Grav. 15 (1998), 1827-1858.
35. R Oeckl, Schrödinger's cat and the clock: Lessons for quantum gravity, Class. Quantum Grav. 20 (2003) 5371-5380
36. R Oeckl, A "general boundary" formulation for quantum mechanics and quantum gravity, Phys. Lett. B 575 (2003) 318-324
37. D Williams, JF Cornwell, The Haar Integral for Lie Supergroups, J.Math.Phys. 25 (1984) 2922
38. Y Ling, L Smolin, Supersymmetric Spin Networks and Quantum Super-gravity, Phys.Rev. D61 (2000) 044008
39. Y Ling, Introduction to supersymmetric spin networks, J.Math.Phys. 43 (2002) 154-169
40. T Thiemann, Kinematical Hilbert Spaces for Fermionic and Higgs Quantum Field Theories, Class.Quant.Grav. 15 (1998) 1487-1512
41. J Roberts, Skein theory and Turaev-Viro invariants, Topology 34 (1995) 771-787
42. HC Lee, RB Zhang, Lickorish Ibvariant and Quantum OSp(1|2)
43. q(1|2)
44. S Davids, Semiclassical Limits of Extended Racah Coefficients, J.Math.Phys. 41 (2000) 924-943; A State Sum Model for (2+1) Lorentzian Quantum Gravity
45. L Freidel, A Ponzano-Regge model of Lorentzian 3-Dimensional gravity, gr-qc/0102098, Nucl.Phys.Proc.Suppl. 88 (2000) 237-240
46. E Witten, Topology-changing amplitudes in (2+1)-dimensional gravity, Nucl. Phys. B 323 (1989) 113-140