Further results on geometric operators in quantum gravity

Classical and Quantum Gravity

Volumn 14, Issue 7, 1997, Pages 1725-1741

  Loll, R ^a,b  

^a ALBERT EINSTEIN INSTITUT   (Germany)

^b Erwin Schrodinger International Institute for Mathematical Physics   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031487008     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/14/7/010     Document Type: Article

References (35)

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7. Loll R 1995 The volume operator in discretized quantum gravity Phys. Rev. Lett. 75 3048-51
8. Loll R 1996 Spectrum of the volume operator in quantum gravity Nucl. Phys. B 460 143-54
9. Loll R Imposing del E > 0 in discrete quantum gravity Phys. Lett. B to appear
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12. Thiemann T 1996 Anomaly-free formulation of nonperturbative four-dimensional Lorentzian quantum gravity Phys. Lett. 380B 257-64 Thiemann T 1996 Quantum spin dynamics I, II Harvard University preprints HUTMP-96/B-351 and B-352
13. Thiemann T 1996 Anomaly-free formulation of nonperturbative four-dimensional Lorentzian quantum gravity Phys. Lett. 380B 257-64 Thiemann T 1996 Quantum spin dynamics I, II Harvard University preprints HUTMP-96/B-351 and B-352
14. Ashtekar A and Lewandowski J 1997 Quantum theory of geometry I: area operators Class. Quantum Grav. 14 A55-81
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16. See, for example, Barreira M, Carfora M and Rovelli C 1996 Physics with nonperturbative quantum gravity: radiation from a quantum black hole Pittsburgh University preprint
17. See, for example, Ashtekar A, Rovelli C and Smolin L 1992 Weaving a classical geometry with quantum threads Phys. Rev. Lett. 69 237-40 Smolin L 1992 Recent developments in nonperturbative quantum gravity Quantum Gravity and Cosmology ed J Pérez-Mercader et al (Singapore: World Scientific) pp 3-84
18. See, for example, Ashtekar A, Rovelli C and Smolin L 1992 Weaving a classical geometry with quantum threads Phys. Rev. Lett. 69 237-40 Smolin L 1992 Recent developments in nonperturbative quantum gravity Quantum Gravity and Cosmology ed J Pérez-Mercader et al (Singapore: World Scientific) pp 3-84
19. Rovelli C and Smolin L 1995 Spin networks and quantum gravity Phys. Rev. D 52 5743-59 Baez J B 1996 Spin network states in gauge theory Adv. Math. 117 253-72 Baez J B 1996 Spin networks and nonperturbative quantum gravity The Interface of Knots and Physics ed L Kauffman (Providence, RI: American Mathematical Society)
20. Rovelli C and Smolin L 1995 Spin networks and quantum gravity Phys. Rev. D 52 5743-59 Baez J B 1996 Spin network states in gauge theory Adv. Math. 117 253-72 Baez J B 1996 Spin networks and nonperturbative quantum gravity The Interface of Knots and Physics ed L Kauffman (Providence, RI: American Mathematical Society)
21. Rovelli C and Smolin L 1995 Spin networks and quantum gravity Phys. Rev. D 52 5743-59 Baez J B 1996 Spin network states in gauge theory Adv. Math. 117 253-72 Baez J B 1996 Spin networks and nonperturbative quantum gravity The Interface of Knots and Physics ed L Kauffman (Providence, RI: American Mathematical Society)
22. Renteln P and Smolin L 1989 A lattice approach to spinorial quantum gravity Class. Quantum Grav. 6 275-94 Renteln P 1990 Some results of SU (2) spinorial lattice gravity Class. Quantum Grav. 7 493-502 Boström O, Miller M and Smolin L A new discretization of classical and quantum general relativity Syracuse University preprint SU-GP-93-4-1 Loll R 1995 Non-perturbative solutions for lattice quantum gravity Nucl. Phys. B 444 619-39 Ezawa K 1996 Multi-plaquette solutions for discretized Ashtekar gravity Mod. Phys. Lett. A 11 2921-32 Fort H, Gambini R and Pullin J Lattice knot theory and quantum gravity in the loop representation Penn State University preprint CGPG-96/8-1
23. Renteln P and Smolin L 1989 A lattice approach to spinorial quantum gravity Class. Quantum Grav. 6 275-94 Renteln P 1990 Some results of SU (2) spinorial lattice gravity Class. Quantum Grav. 7 493-502 Boström O, Miller M and Smolin L A new discretization of classical and quantum general relativity Syracuse University preprint SU-GP-93-4-1 Loll R 1995 Non-perturbative solutions for lattice quantum gravity Nucl. Phys. B 444 619-39 Ezawa K 1996 Multi-plaquette solutions for discretized Ashtekar gravity Mod. Phys. Lett. A 11 2921-32 Fort H, Gambini R and Pullin J Lattice knot theory and quantum gravity in the loop representation Penn State University preprint CGPG-96/8-1
24. Renteln P and Smolin L 1989 A lattice approach to spinorial quantum gravity Class. Quantum Grav. 6 275-94 Renteln P 1990 Some results of SU (2) spinorial lattice gravity Class. Quantum Grav. 7 493-502 Boström O, Miller M and Smolin L A new discretization of classical and quantum general relativity Syracuse University preprint SU-GP-93-4-1 Loll R 1995 Non-perturbative solutions for lattice quantum gravity Nucl. Phys. B 444 619-39 Ezawa K 1996 Multi-plaquette solutions for discretized Ashtekar gravity Mod. Phys. Lett. A 11 2921-32 Fort H, Gambini R and Pullin J Lattice knot theory and quantum gravity in the loop representation Penn State University preprint CGPG-96/8-1
25. Renteln P and Smolin L 1989 A lattice approach to spinorial quantum gravity Class. Quantum Grav. 6 275-94 Renteln P 1990 Some results of SU (2) spinorial lattice gravity Class. Quantum Grav. 7 493-502 Boström O, Miller M and Smolin L A new discretization of classical and quantum general relativity Syracuse University preprint SU-GP-93-4-1 Loll R 1995 Non-perturbative solutions for lattice quantum gravity Nucl. Phys. B 444 619-39 Ezawa K 1996 Multi-plaquette solutions for discretized Ashtekar gravity Mod. Phys. Lett. A 11 2921-32 Fort H, Gambini R and Pullin J Lattice knot theory and quantum gravity in the loop representation Penn State University preprint CGPG-96/8-1
26. Renteln P and Smolin L 1989 A lattice approach to spinorial quantum gravity Class. Quantum Grav. 6 275-94 Renteln P 1990 Some results of SU (2) spinorial lattice gravity Class. Quantum Grav. 7 493-502 Boström O, Miller M and Smolin L A new discretization of classical and quantum general relativity Syracuse University preprint SU-GP-93-4-1 Loll R 1995 Non-perturbative solutions for lattice quantum gravity Nucl. Phys. B 444 619-39 Ezawa K 1996 Multi-plaquette solutions for discretized Ashtekar gravity Mod. Phys. Lett. A 11 2921-32 Fort H, Gambini R and Pullin J Lattice knot theory and quantum gravity in the loop representation Penn State University preprint CGPG-96/8-1
27. Renteln P and Smolin L 1989 A lattice approach to spinorial quantum gravity Class. Quantum Grav. 6 275-94 Renteln P 1990 Some results of SU (2) spinorial lattice gravity Class. Quantum Grav. 7 493-502 Boström O, Miller M and Smolin L A new discretization of classical and quantum general relativity Syracuse University preprint SU-GP-93-4-1 Loll R 1995 Non-perturbative solutions for lattice quantum gravity Nucl. Phys. B 444 619-39 Ezawa K 1996 Multi-plaquette solutions for discretized Ashtekar gravity Mod. Phys. Lett. A 11 2921-32 Fort H, Gambini R and Pullin J Lattice knot theory and quantum gravity in the loop representation Penn State University preprint CGPG-96/8-1
28. Thiemann T A length operator for canonical quantum gravity Harvard University preprint HUTMP-96/B-354
29. Kogut J and Susskind L 1975 Hamiltonian formulation of Wilson's lattice gauge theories Phys. Rev. D 11 395-408 Kogut J B 1983 The lattice gauge theory approach to quantum chromodynamics Rev. Mod. Phys. 55 775-836
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31. Ashtekar A and Lewandowski J 1995 Differential geometry on the spaces of connections via graphs J. Geom. Phys. 17 191-230
32. Lewandowski J 1996 Volume and quantizations Warsaw University preprint
33. Ashtekar A 1996 Talk given at ESI workshop and private communication
34. Smolin L The classical limit and the form of the hamiltonian constraint in nonperturbative quantum gravity, Penn State University preprint CGPG-96/9-4
35. Loll R in preparation