Coherent states for canonical quantum general relativity and the infinite tensor product extension

Nuclear Physics B

Volumn 606, Issue 1-2, 2001, Pages 401-440

  Sahlmann, H ^a   Thiemann, T ^a   Winkler, O ^a  

^a ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035833231     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(01)00226-7     Document Type: Article

References (69)

1. Ashtekar A. Non-Perturbative Canonical Gravity. 1991;World Scientific, Singapore.
2. Ashtekar A. Julia B. Gravitation and Quantization. 1995;Elsevier, Amsterdam.
3. Rovelli C. Loop quantum gravity. Review written for electronic journal "Living Reviews" gr-qc/9710008.
4. Rovelli C. Strings, loops and others: a critical survey of the present approaches to quantum gravity. Plenary lecture given at 15th Int. Conf. on Gen. Rel. and Gravitation (GR15), Pune, India, Dec. 16-21, 1997 gr-qc/9803024.
5. Ashtekar A., Beetle C., Dreyer O., Fairhurst S., Krishnan B., Lewandowski J., Wisniewski J. Phys. Rev. Lett. 85:2000;3564-3567 gr-qc/0006006.
6. Baez J. Lect. Notes Phys. 543:2000;25.
7. Gambini R., Pullin J. Phys. Rev. D. 59:1999;124021.
8. Alfaro J., Morales-Tecotl H.A., Urrutia L.F. Phys. Rev. Lett. 84:2000;2318-2321.
9. Varadarajan M., Zapata J.-A. Class. Quantum Grav. 17:2000;4085 gr-qc/0001040.
10. Arnsdorf M. Approximating connections in loop quantum gravity. gr-qc/9910084.
11. Arnsdorf M., Gupta S. Nucl. Phys. B. 577:2000;529.
12. Corichi A. A Gaussian weave for kinematical loop quantum gravity. gr-qc/0006067.
13. Thiemann T. Symplectic structures and continuum lattice formulations of gauge field theories. hep-th/0005232.
14. Thiemann T. Gauge field theory coherent states (GCS): I. General framework. hep-th/0005233.
15. Thiemann T., Winkler O. Gauge field theory coherent states (GCS): II. Peakedness properties. hep-th/0005237.
16. Thiemann T., Winkler O. Gauge field theory coherent states (GCS): III. Ehrenfest theorems. hep-th/0005234.
17. Thiemann T., Winkler O. Gauge field theory coherent states (GCS): IV. Infinite tensor product and thermodynamic limit. hep-th/0005235.
18. Rovelli C., Smolin L. Nucl. Phys. B. 442:1995;593.
19. Rovelli C., Smolin L. Nucl. Phys. B. 456:1995;734. Erratum.
20. Ashtekar A., Lewandowski J. Class. Quantum Grav. 14:1997;A55-81.
21. A. Ashtekar, L. Bombelli, Statistical Geometry and Semiclassical Quantum Gravity, to appear.
22. Itzykson C., Drouffe J.-M. Statistical Field Theory. 2:1997;Cambridge Univ. Press, Cambridge.
23. Ashtekar A., Rovelli C., Smolin L. Phys. Rev. Lett. 69:1992;237.
24. Rovelli C., Smolin L. Phys. Rev. D. 52:1995;5743.
25. Baez J. Adv. Math. 117:1996;253.
26. T. Thiemann, Quantum spin dynamics (QSD): VIII. The classical limit, in preparation.
27. Ashtekar A., Lewandowski J., Marolf D., Mourão J., Thiemann T. J. Math. Phys. 36:1995;6456-6493 gr-qc/9504018.
28. Thiemann T. Phys. Lett. B. 380:1996;257-264 gr-qc/960688.
29. Thiemann T. Class. Quantum Grav. 15:1998;839-873 gr-qc/9606089.
30. Thiemann T. Class. Quantum Grav. 15:1998;875-905 gr-qc/9606090.
31. Thiemann T. Class. Quantum Gravity. 15:1998;1207-1247 gr-qc/9705017.
32. Thiemann T. Class. Quantum Grav. 15:1998;1249-1280 gr-qc/9705018.
33. Thiemann T. Class. Quantum Grav. 15:1998;1281-1314 gr-qc/9705019.
34. Thiemann T. Class. Quantum Grav. 15:1998;1487-1512 gr-qc/9705021.
35. Di Bartolo C., Gambini R., Griego J., Pullin J. Phys. Rev. Lett. 84:2000;2314.
36. Di Bartolo C., Gambini R., Griego J., Pullin J. Class. Quant. Grav. 17:2000;3211.
37. Di Bartolo C., Gambini R., Griego J., Pullin J. Class. Quant. Grav. 17:2000;3239.
38. Ashtekar A., Lewandowski J., Marolf D., Mourão J., Thiemann T. J. Funct. Analysis. 135:1996;519-551 gr-qc/9412014.
39. A. Ashtekar, L. Bombelli, O. Dreyer, S. Fairhurst, A. Gupta, H. Sahlmann, T. Thiemann, O. Winkler, Kinematical versus Dynamical Coherent States, in preparation.
40. H. Sahlmann, T. Thiemann, O. Winkler, Canonical Quantum General Relativity and Algebraic Graph Theory, in preparation.
41. Biggs N. Algebraic Graph Theory. 2nd edn. 1993;Cambridge Univ. Press, Cambridge.
42. Stauffer D., Aharony A. Introduction to Percolation Theory, Taylor and Francis. 2nd edn. 1994;London.
43. Cvetovic D.M., Doob M., Sachs H. Spectra of Graphs. 1979;Academic Press, New York.
44. Hall B.C. J. Funct. Analysis. 122:1994;103.
45. Hall B.C. Commun. Math. Phys. 184:1997;233-250.
46. Ashtekar A., Isham C.J. Class. Quantum Grav. 9:1992;1433.
47. C algebras. Baez J. Knots and Quantum Gravity. 1994;Oxford Univ. Press, Oxford.
48. Ashtekar A., Lewandowski J. J. Geo. Physics. 17:1995;191.
49. Ashtekar A., Lewandowski J. J. Math. Phys. 36:1995;2170.
50. Baez J., Sawin S. Functional integration on spaces of connections. q-alg/9507023.
51. Baez J., Sawin S. Diffeomorphism invariant spin-network states. q-alg/9708005.
52. Lewandowski J., Thiemann T. Class. Quantum Grav. 16:1999;2299-2322 gr-qc/9901015.
53. von Neumann J. Comp. Math. 6:1938;1-77.
54. Thirring W. Lehrbuch der Mathematischen Physik. 4:1994;Springer-Verlag, Wien.
55. Connes A. Noncommutative Geometry. 1994;Academic Press.
56. Haag R. Local Quantum Physics. 2nd edn. 1996;Springer-Verlag, Berlin.
57. Yamasaki Y. Measures on Infinite Dimensional Spaces. 1985;World Scientific, Singapore.
58. H. Sahlmann, T. Thiemann, Quantum Field Theory on Curved Spacetimes from Canonical Quantum General Relativity: I. Scalar Fields, II. Photons and the γ Ray Burst Effect, III. Gravitons, to appear.
59. Bojowald M., Kastrup H. Class. Quantum Grav. 17:2000;3009 hep-th/9907042.
60. Bojowald M., Kastrup H. Class. Quantum Grav. 17:2000;3044 hep-th/9907043.
61. Bojowald M. J. Math. Phys. 41:2000;4313 hep-th/9908170.
62. Bojowald M. Class. Quantum Grav. 17:2000;1489 gr-qc/9910103.
63. Bojowald M. Class. Quantum Grav. 17:2000;1509 gr-qc/9910104.
64. Bojowald M. gr-qc/0008052.
65. Bojowald M. gr-qc/0008053.
66. Bojowald M. Absence of singularity in loop quantum cosmology. gr-qc/0102069.
67. Ashtekar A., Lewandowski J. Adv. Theor. Math. Phys. 1:1997;388.
68. Whittaker E.T., Watson G.N. A Course of Modern Analysis. 1969;Cambridge Univ. Press, Cambridge. Chapter VII.
69. Jeffreys H., Jeffreys B.S. Methods of Mathematical Physics. 1992;Cambridge Univ. Press, Cambridge.