Gauge field theory coherent states (GCS): I. General properties

Classical and Quantum Gravity

Volumn 18, Issue 11, 2001, Pages 2025-2064

  Thiemann, Thomas ^a  

^a ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035532879     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/18/11/304     Document Type: Article

References (111)

1. Horowitz G 2000 Quantum gravity at the turn of the millenium Preprint gr-qc/0011089 Rovelli C 2000 Notes for a brief history of quantum gravity Preprint gr-qc/0006061
2. Horowitz G 2000 Quantum gravity at the turn of the millenium Preprint gr-qc/0011089 Rovelli C 2000 Notes for a brief history of quantum gravity Preprint gr-qc/0006061
3. Ashtekar A 1986 Phys. Rev. Lett. 57 2244 Ashtekar A 1987 Phys. Rev. D 36 1587
4. Ashtekar A 1986 Phys. Rev. Lett. 57 2244 Ashtekar A 1987 Phys. Rev. D 36 1587
5. Ashtekar A 1987 Mathematics and General Relativity (Providence, RI: American Mathematical Society)
6. Barbero F 1995 Phys. Rev. D 51 5507 Barbero F 1995 Phys. Rev. D 51 5498
7. Barbero F 1995 Phys. Rev. D 51 5507 Barbero F 1995 Phys. Rev. D 51 5498
8. Thiemann T 1996 Phys. Lett. B 380 257-64 (Thiemann T 1996 Preprint gr-qc/9606088)
9. Gambini R and Trias A 1980 Phys. Rev. D 22 1380 Di Bartolo C, Nori F, Gambini R and Trias A 1983 Lett. Nuovo Cimento 38 497 Gambini R and Trias A 1986 Nucl. Phys. B 278 436
10. Gambini R and Trias A 1980 Phys. Rev. D 22 1380 Di Bartolo C, Nori F, Gambini R and Trias A 1983 Lett. Nuovo Cimento 38 497 Gambini R and Trias A 1986 Nucl. Phys. B 278 436
11. Gambini R and Trias A 1980 Phys. Rev. D 22 1380 Di Bartolo C, Nori F, Gambini R and Trias A 1983 Lett. Nuovo Cimento 38 497 Gambini R and Trias A 1986 Nucl. Phys. B 278 436
12. Rovelli C and Smolin L 1990 Nucl. Phys. B 331 80
13. Ashtekar A and Isham C J 1992 Class. Quantum Grav. 9 1433
14. Ashtekar A, Lewandowski J 1994 Representation theory of analytic holonomy C* algebras Knots and Quantum Gravity ed J Baez (Oxford: Oxford University Press) Ashtekar A and Lewandowski J 1995 J. Geo. Phys. 17 191 Ashtekar A and Lewandowski J 1995 J. Math. Phys. 36 2170
15. Ashtekar A, Lewandowski J 1994 Representation theory of analytic holonomy C* algebras Knots and Quantum Gravity ed J Baez (Oxford: Oxford University Press) Ashtekar A and Lewandowski J 1995 J. Geo. Phys. 17 191 Ashtekar A and Lewandowski J 1995 J. Math. Phys. 36 2170
16. Ashtekar A, Lewandowski J 1994 Representation theory of analytic holonomy C* algebras Knots and Quantum Gravity ed J Baez (Oxford: Oxford University Press) Ashtekar A and Lewandowski J 1995 J. Geo. Phys. 17 191 Ashtekar A and Lewandowski J 1995 J. Math. Phys. 36 2170
17. Marolf D and J. M. Mourão 1995 Commun. Math. Phys. 170 583-606
18. Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T 1995 J. Math. Phys. 36 6456-93 (Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T 1995 Preprint gr-qc/9504018)
19. de Pietri R and Rovelli C 1996 Phys. Rev. D 54 2664
20. Gambini R and Pullin J 1996 Loops, Knots, Gauge Theories and Quantum Gravity (Cambridge: Cambridge University Press)
21. Thiemann T 1998 J. Math. Phys. 39 1236-48 (Thiemann T 1996 Preprint hep-th/9601105)
22. de Pietri R 1997 Class. Quantum Grav. 14 53
23. Thiemann T 1998 J. Math. Phys. 39 3372-92 (Thiemann T 1996 Preprint gr-qc/9606092)
24. Rovelli C and Smolin L 1995 Nucl. Phys. B 442 593 Rovelli C and Smolin L 1995 Nucl. Phys. B 456 734 (erratum)
25. Rovelli C and Smolin L 1995 Nucl. Phys. B 442 593 Rovelli C and Smolin L 1995 Nucl. Phys. B 456 734 (erratum)
26. Ashtekar A and Lewandowski J 1997 Class. Quantum Grav. 14 A55-81
27. Loll R 1996 Nucl. Phys. B 460 143 Loll R 1997 Class. Quantum Grav. 14 1725 Loll R 1997 Nucl. Phys. B 500 405
28. Loll R 1996 Nucl. Phys. B 460 143 Loll R 1997 Class. Quantum Grav. 14 1725 Loll R 1997 Nucl. Phys. B 500 405
29. Loll R 1996 Nucl. Phys. B 460 143 Loll R 1997 Class. Quantum Grav. 14 1725 Loll R 1997 Nucl. Phys. B 500 405
30. Ashtekar A and Lewandowski J 1997 Adv. Theor. Math. Phys. 1 388-429
31. Thiemann T 1998 J. Math. Phys. 39 3347-71 (Thiemann T 1996 Preprint gr-qc/9606091)
32. Thiemann T 1998 Class. Quantum Grav. 15 839-73 (Thiemann T 1996 Preprint gr-qc/9606089)
33. Thiemann T 1998 Class. Quantum Grav. 15 875-905 (Thiemann T 1996 Preprint gr-qc/9606090)
34. Thiemann T 1998 Class. Quantum Grav. 15 1249-80 (Thiemann T 1997 Preprint gr-qc/9705018)
35. Thiemann T 1998 Class. Quantum Grav. 15 1281-314 (Thiemann T 1997 Preprint gr-qc/9705019)
36. Thiemann T 1998 Class. Quantum Grav. 15 1487-512 (Thiemann T 1997 Preprint gr-qc/9705021)
37. Thiemann T 1998 Class. Quantum Grav. 15 1463-85 (Thiemann T 1997 Preprint gr-qc/9705020)
38. Thiemann T 1998 Class. Quantum Grav. 15 1207-47 (Thiemann T 1997 Preprint gr-qc/9705017)
39. Bojowald M 2000 J. Math. Phys. 41 4313 Bojowald M 2000 Class. Quantum Grav. 17 1489 Bojowald M 2000 Class. Quantum Grav. 17 1509 Bojowald M 2001 Class. Quantum Grav. 18 1055-70 (Bojowald M 2000 Preprint gr-qc/0008052) Bojowald M 2001 Class. Quantum Grav. 18 1071-88 (Bojowald M 2000 Preprint gr-qc/0008053) Bojowald M 2001 Absence of singularity in loop quantum cosmology Preprint gr-qc/0102069
40. Bojowald M 2000 J. Math. Phys. 41 4313 Bojowald M 2000 Class. Quantum Grav. 17 1489 Bojowald M 2000 Class. Quantum Grav. 17 1509 Bojowald M 2001 Class. Quantum Grav. 18 1055-70 (Bojowald M 2000 Preprint gr-qc/0008052) Bojowald M 2001 Class. Quantum Grav. 18 1071-88 (Bojowald M 2000 Preprint gr-qc/0008053) Bojowald M 2001 Absence of singularity in loop quantum cosmology Preprint gr-qc/0102069
41. Bojowald M 2000 J. Math. Phys. 41 4313 Bojowald M 2000 Class. Quantum Grav. 17 1489 Bojowald M 2000 Class. Quantum Grav. 17 1509 Bojowald M 2001 Class. Quantum Grav. 18 1055-70 (Bojowald M 2000 Preprint gr-qc/0008052) Bojowald M 2001 Class. Quantum Grav. 18 1071-88 (Bojowald M 2000 Preprint gr-qc/0008053) Bojowald M 2001 Absence of singularity in loop quantum cosmology Preprint gr-qc/0102069
42. Bojowald M 2000 J. Math. Phys. 41 4313 Bojowald M 2000 Class. Quantum Grav. 17 1489 Bojowald M 2000 Class. Quantum Grav. 17 1509 Bojowald M 2001 Class. Quantum Grav. 18 1055-70 (Bojowald M 2000 Preprint gr-qc/0008052) Bojowald M 2001 Class. Quantum Grav. 18 1071-88 (Bojowald M 2000 Preprint gr-qc/0008053) Bojowald M 2001 Absence of singularity in loop quantum cosmology Preprint gr-qc/0102069
43. Bojowald M 2000 J. Math. Phys. 41 4313 Bojowald M 2000 Class. Quantum Grav. 17 1489 Bojowald M 2000 Class. Quantum Grav. 17 1509 Bojowald M 2001 Class. Quantum Grav. 18 1055-70 (Bojowald M 2000 Preprint gr-qc/0008052) Bojowald M 2001 Class. Quantum Grav. 18 1071-88 (Bojowald M 2000 Preprint gr-qc/0008053) Bojowald M 2001 Absence of singularity in loop quantum cosmology Preprint gr-qc/0102069
44. Bojowald M 2000 J. Math. Phys. 41 4313 Bojowald M 2000 Class. Quantum Grav. 17 1489 Bojowald M 2000 Class. Quantum Grav. 17 1509 Bojowald M 2001 Class. Quantum Grav. 18 1055-70 (Bojowald M 2000 Preprint gr-qc/0008052) Bojowald M 2001 Class. Quantum Grav. 18 1071-88 (Bojowald M 2000 Preprint gr-qc/0008053) Bojowald M 2001 Absence of singularity in loop quantum cosmology Preprint gr-qc/0102069
45. Di Bartolo C, Gambini R, Griego J and Pullin J 2000 Phys. Rev. Lett. 84 2314 Di Bartolo C, Gambini R, Griego J and Pullin J 2000 Class. Quantum Grav. 17 3211 Di Bartolo C, Gambini R, Griego J and Pullin J 2000 Class. Quantum Grav. 17 3239
46. Di Bartolo C, Gambini R, Griego J and Pullin J 2000 Phys. Rev. Lett. 84 2314 Di Bartolo C, Gambini R, Griego J and Pullin J 2000 Class. Quantum Grav. 17 3211 Di Bartolo C, Gambini R, Griego J and Pullin J 2000 Class. Quantum Grav. 17 3239
47. Di Bartolo C, Gambini R, Griego J and Pullin J 2000 Phys. Rev. Lett. 84 2314 Di Bartolo C, Gambini R, Griego J and Pullin J 2000 Class. Quantum Grav. 17 3211 Di Bartolo C, Gambini R, Griego J and Pullin J 2000 Class. Quantum Grav. 17 3239
48. Reisenberger M and Rovelli C 1997 Phys. Rev. D 56 3490-508
49. Baez J 1998 Class. Quantum Grav. 15 1827-58 Baez J 2000 Lecture Notes in Physics vol 543, p 25
50. Baez J 1998 Class. Quantum Grav. 15 1827-58 Baez J 2000 Lecture Notes in Physics vol 543, p 25
51. Markopoulou F and Smolin L 1998 Phys. Rev. D 58 084032 Markopoulou F 2000 Class. Quantum Grav. 17 2059
52. Markopoulou F and Smolin L 1998 Phys. Rev. D 58 084032 Markopoulou F 2000 Class. Quantum Grav. 17 2059
53. Barrett J W and Crane L 1997 Class. Quantum Grav. 14 2113 Barrett J W 2000 State sum models and quantum gravity Preprint gr-qc/0010050
54. Barrett J W and Crane L 1997 Class. Quantum Grav. 14 2113 Barrett J W 2000 State sum models and quantum gravity Preprint gr-qc/0010050
55. Freidel L and Krasnov K 1999 Adv. Theor. Math. Phys. 2 1183
56. Krasnov K 1998 Gen. Rel. Grav. 30 53-68
57. Ashtekar A, Beetle C and Fairhurst S 2000 Class. Quantum Grav. 17 1317
58. Ashtekar A, Corichi A and Krasnov K 2000 Isolated horizons: the classical phase space Adv. Theor. Math. Phys. 3419-78 (Ashtekar A, Corichi A and Krasnov K 1999 Preprint gr-qc/9905089)
59. Ashtekar A, Beetle C and Fairhurst S 2000 Class. Quantum Grav. 16 L1-L7 (Ashtekar A, Beetle C and Fairhurst S 1998 Preprint gr-qc/9812065)
60. Ashtekar A and Krasnov K 1998 Quantum geometry and black holes Preprint gr-qc/9804039
61. Ashtekar A, Baez J, Corichi A and Krasnov K 1998 Phys. Rev. Lett. 80 904
62. Ashtekar A 2000 Interface of general relativity, quantum physics and statistical mechanics: some recent developments Ann. Phys., Lpz. 9 178-98 (Ashtekar A 1999 Preprint gr-qc/9910101)
63. Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): II. Peakedness properties Class. Quantum Grav. to appear (Thiemann T and Winkler O 2000 Preprint hep-th/0005237)
64. Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): III. Ehrenfest theorems Class. Quantum Grav. submitted (Thiemann T and Winkler O 2000 Preprint hep-th/0005234)
65. Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): IV. Infinite tensor product and thermodynamic limit Class. Quantum Grav. submitted (Thiemann T and Winkler O 2000 Preprint hep-th/0005235)
66. Thiemann T 2001 Gauge field theory coherent states (GCS): V. Extension to Higgs fields and fermions to appear
67. Sahlmann H and Thiemann T 2001 Quantum field theory in curved spacetimes from canonical quantum general relativity: I. Scalar fields, to appear Sahlmann H and Thiemann T 2001 Quantum field theory in curved spacetimes from canonical quantum general relativity: II. Photons and the γ ray burst effect, to appear Sahlmann H and Thiemann T 2001 Quantum field theory in curved spacetimes from canonical quantum general relativity: III. Gravitons, to appear
68. Sahlmann H and Thiemann T 2001 Quantum field theory in curved spacetimes from canonical quantum general relativity: I. Scalar fields, to appear Sahlmann H and Thiemann T 2001 Quantum field theory in curved spacetimes from canonical quantum general relativity: II. Photons and the γ ray burst effect, to appear Sahlmann H and Thiemann T 2001 Quantum field theory in curved spacetimes from canonical quantum general relativity: III. Gravitons, to appear
69. Sahlmann H and Thiemann T 2001 Quantum field theory in curved spacetimes from canonical quantum general relativity: I. Scalar fields, to appear Sahlmann H and Thiemann T 2001 Quantum field theory in curved spacetimes from canonical quantum general relativity: II. Photons and the γ ray burst effect, to appear Sahlmann H and Thiemann T 2001 Quantum field theory in curved spacetimes from canonical quantum general relativity: III. Gravitons, to appear
70. Sahlmann H, Thiemann T and Winkler O 2001 Coherent states for canonical quantum general relativity and the infinite tensor product extension (Sahlmann H, Thiemann T and Winkler O 2001 Preprint gr-qc/0102038)
71. Thiemann T 1996 Class. Quantum Grav. 13 1383-403 (Thiemann T 1995 Preprint gr-qc/9511057) Thiemann T 1995 Acta Cosmologica 21 145-67 (Thiemann T 1995 Preprint gr-qc/9511049) Thiemann T 1996 Symplectic Singularities and Geometry of Gauge Fields (Warsaw: Banach Center Publications) vol 39, pp 389-403 (Thiemann T 1995 Preprint hep-th/9511122)
72. Thiemann T 1996 Class. Quantum Grav. 13 1383-403 (Thiemann T 1995 Preprint gr-qc/9511057) Thiemann T 1995 Acta Cosmologica 21 145-67 (Thiemann T 1995 Preprint gr-qc/9511049) Thiemann T 1996 Symplectic Singularities and Geometry of Gauge Fields (Warsaw: Banach Center Publications) vol 39, pp 389-403 (Thiemann T 1995 Preprint hep-th/9511122)
73. Thiemann T 1996 Class. Quantum Grav. 13 1383-403 (Thiemann T 1995 Preprint gr-qc/9511057) Thiemann T 1995 Acta Cosmologica 21 145-67 (Thiemann T 1995 Preprint gr-qc/9511049) Thiemann T 1996 Symplectic Singularities and Geometry of Gauge Fields (Warsaw: Banach Center Publications) vol 39, pp 389-403 (Thiemann T 1995 Preprint hep-th/9511122)
74. Hall B C 1994 J. Funct. Anal. 122 103 Hall B 1997 Commun. Math. Phys. 184 233-50
75. Hall B C 1994 J. Funct. Anal. 122 103 Hall B 1997 Commun. Math. Phys. 184 233-50
76. Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T 1996 J. Funct. Anal. 135 519-51 (Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T 1994 Preprint gr-qc/9412014)
77. von Neumann J 1938 Comput. Math. 6 1-77 Thirring W 1994 Lehrbuch der Mathematischen Physik vol 4, (Vienna: Springer)
78. von Neumann J 1938 Comput. Math. 6 1-77 Thirring W 1994 Lehrbuch der Mathematischen Physik vol 4, (Vienna: Springer)
79. Klauder J R and Skagerstam B-S 1985 Coherent States (Singapore: World Scientific) Perelomov A 1986 Generalized Coherent States and Their Applications (Berlin: Springer)
80. Klauder J R and Skagerstam B-S 1985 Coherent States (Singapore: World Scientific) Perelomov A 1986 Generalized Coherent States and Their Applications (Berlin: Springer)
81. Amelino-Camelia G et al 1998 Nature 393 763
82. Biller S D et al 1999 Phys. Rev. Lett. 83 2108
83. Gambini R and Pullin J 1999 Phys. Rev. D 59 124021 Alfaro J, Morales-Tecotl H A and Urrutia L F 2000 Phys. Rev. Lett. 84 2318-21 (Alfaro J, Morales-Tecotl H A and Urrutia L F 1999 Preprint gr-qc/9909079)
84. Gambini R and Pullin J 1999 Phys. Rev. D 59 124021 Alfaro J, Morales-Tecotl H A and Urrutia L F 2000 Phys. Rev. Lett. 84 2318-21 (Alfaro J, Morales-Tecotl H A and Urrutia L F 1999 Preprint gr-qc/9909079)
85. Ashtekar A, Rovelli C and Smolin L 1992 Phys. Rev. Lett. 69 237
86. Thiemann T 2001 Quantum spin dynamics (QSD): VIII. The classical limit to appear
87. Ashtekar A and Bombelli L 2001 Statistical geometry and semiclassical quantum gravity, in preparation
88. Thiemann T 2000 Quantum spin dynamics (QSD): VII. Symplectic structures and continuum lattice formulations of gauge field theories Class. Quantum Grav. submitted (Thiemann T 2000 Preprint hep-th/0005232)
89. Hebey E 1996 Sobolev Spaces on Riemannian Manifolds (Lecture Notes in Mathematics vol 1635) (Berlin: Springer)
90. Lang S 1972 Differential Manifolds (Reading, MA: Addison-Wesley)
91. Baez J and Sawin S 1995 Functional integration on spaces of connections Preprint q-alg/9507023 Baez J and Sawin S 1997 Diffeomorphism invariant spin-network states Preprint q-alg/9708005
92. Baez J and Sawin S 1995 Functional integration on spaces of connections Preprint q-alg/9507023 Baez J and Sawin S 1997 Diffeomorphism invariant spin-network states Preprint q-alg/9708005
93. Lewandowski J and Thiemann T 1999 Class. Quantum Grav. 16 2299-322 (Lewandowski J and Thiemann T 1999 Preprint gr-qc/9901015)
94. Rovelli C and Smolin L 1995 Phys. Rev. D 52 5743 (Rovelli C and Smolin L 1995 Spin networks and quantum gravity Preprint CGPG-95/4-1)
95. Rovelli C and Smolin L 1995 Phys. Rev. D 52 5743 (Rovelli C and Smolin L 1995 Spin networks and quantum gravity Preprint CGPG-95/4-1)
96. Baez J 1996, Adv. Math. 117 253-72
97. Rendall A 1993 Class. Quantum Grav. 10 605 Rendall A 1994 Adjointness relations as a criterion for choosing an inner product Preprint gr-qc/9403001
98. Rendall A 1993 Class. Quantum Grav. 10 605 Rendall A 1994 Adjointness relations as a criterion for choosing an inner product Preprint gr-qc/9403001
99. Velhinho J 2000 A groupoid approach to spaces of generalized connections Preprint hep-th/0011200
100. Yamasaki Y 1985 Measures on Infinite Dimensional Spaces (Singapore: World Scientific)
101. Giles R 1981 Phys. Rev. D 8 2160
102. Ashtekar A and Lewandowski J 1993 Class. Quantum Grav. 10 L69
103. Urakawa H 1975 Osaka J. Math. 12 285-97 Gangolli R 1968 Acta Math. 121 151
104. Urakawa H 1975 Osaka J. Math. 12 285-97 Gangolli R 1968 Acta Math. 121 151
105. Rovelli C and Thiemann T 1998 Phys. Rev. D 57 1009-14 (Rovelli C and Thiemann T 1997 Preprint gr-qc/9705059)
106. Seifert H and Threlfall W 1980 Lehrbuch der Topologie (New York: Chelsea)
107. Bronstein I N and Semendjajew K A 1982 Taschenbuch der Mathematik (Frankfurt: Harri Deutsch)
108. Woodhouse N M J 1991 Geometric Quantization 2nd edn (Oxford: Clarendon)
109. Giulini D and Marolf D 1999 Class. Quantum Grav. 16 2479 Giulini D and Marolf D 1999 Class. Quantum Grav. 16 2489 Gomberoff A and Marolf D 1999 Int. J. Mod. Phys. D 8 519
110. Giulini D and Marolf D 1999 Class. Quantum Grav. 16 2479 Giulini D and Marolf D 1999 Class. Quantum Grav. 16 2489 Gomberoff A and Marolf D 1999 Int. J. Mod. Phys. D 8 519
111. Giulini D and Marolf D 1999 Class. Quantum Grav. 16 2479 Giulini D and Marolf D 1999 Class. Quantum Grav. 16 2489 Gomberoff A and Marolf D 1999 Int. J. Mod. Phys. D 8 519