A uniqueness theorem for constraint quantization

Classical and Quantum Gravity

Volumn 16, Issue 7, 1999, Pages 2489-2505

  Giulini, Domenico ^a,d   Marolf, Donald ^b,c,d  

^a UNIVERSITY OF ZURICH   (Switzerland)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c SYRACUSE UNIVERSITY   (United States)

^d ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033243671     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/16/7/322     Document Type: Article

References (54)

1. Dirac P A M 1964 Lectures on Quantum Mechanics (New York: Belfer Graduate School of Science, Yeshiva University)
2. Ashtekar A 1991 Non-Perturbative Canonical Gravity (Singapore: World Scientific) (lectures notes prepared in collaboration with R S Tate) Julia B (ed) 1995 Gravitation and Quantization (Amsterdam: Elsevier)
3. Ashtekar A 1991 Non-Perturbative Canonical Gravity (Singapore: World Scientific) (lectures notes prepared in collaboration with R S Tate) Julia B (ed) 1995 Gravitation and Quantization (Amsterdam: Elsevier)
4. Kuchǎr K 1992 Time and interpretations of quantum gravity Proc. 4th Canadian Conf. on General Relativity and Relativistic Astrophysics ed G Kunstatter et al (Singapore: World Scientific)
5. Isham C 1995 Structural issues in quantum gravity Proc. Int. Conf. on General Relativity and Gravitation (Florence) pp 167-209 Isham C 1995 Preprint gr-qc/9510063)
6. Isham C 1995 Structural issues in quantum gravity Proc. Int. Conf. on General Relativity and Gravitation (Florence) pp 167-209 (Isham C 1995 Preprint gr-qc/9510063)
7. Rovelli C 1998 Loop quantum gravity Living Rev. Relativity 1 Rovelli C Preprint gr-qc/9710008)
8. Rovelli C 1998 Loop quantum gravity Living Rev. Relativity 1 (Rovelli C Preprint gr-qc/9710008)
9. Misner C W 1969 Mixmaster universe Phys. Rev. Lett. 22 1071-4
10. Misner C, Thorne K and Wheeler J 1973 Gravitation (New York: Freeman) p 805
11. Ryan M and Shepley L 1975 Homogeneous Relativistic Cosmologies (Princeton, NJ: Princeton University Press)
12. Wald R 1993 A proposal for solving the 'problem of time' in quantum gravity Phys. Rev. D 48 R2377-81
13. Banks T, Fischler W and Motl L 1998 Dualities versus singularities Preprint hep-th/9811194
14. Cavaglia M and Ungarelli C 1999 Canonical path integral quantisation of string cosmology models Preprint gr-qc/9902004
15. Woodhouse N 1980 Geometric Quantization (Oxford: Oxford University Press)
16. Tuynman G M 1990 Reduction, quantization and nonunimodular groups J. Math. Phys. 31 83-90
17. Duval C, Elhadad J, Gotay M J and Tuynman G M 1990 Nonunimodularity and the quantization of the pseudo-rigid body Hamiltonian Systems, Transformation Groups and Spectral Transform Methods ed J Harnad and J Marsden (Montreal: Les Publications du CRM) pp 149-60
18. Duval C, Elhadad J, Gotay M J, Śniatycki J and Tuynman G M 1991 Quantization and bosonic BRST theory Ann. Phys., NY 206 1-26
19. Henneaux M and Teitelboim C 1982 Relativistic quantum mechanics and supersymmetric particles Ann. Phys., NY 143 127-59
20. Halliwell J J and Hartle J B 1990 Integration contours for the no-boundary wave function of the universe Phys. Rev. D 41 1815
21. Halliwell J J and Ortiz M E 1993 Sum over histories origin of the composition laws of relativistic quantum mechanics Phys. Rev. D 48 748-68
22. Klauder J 1998 Product representations and the quantization of constrained systems Preprint quant-ph/9811051 (to appear in the Fadeev Festschrift)
23. Klauder J 1998 Coherent state path integrals at (nearly) 40 Proc. Florence Path Integral Conf. Preprint quantph/9810043
24. Grundling H and Hurst C A 1985 Algebraic quantization of systems with a gauge degeneracy Commun. Math. Phys. 98 369-90
25. Grundling H and Lledó 1998 Local quantum constraints Preprint math-ph/9812022
26. Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T 1995 Quantization of diffeomorphism invariant theories of connections with local degrees of freedom J. Math. Phys. 36 6456-93 Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T 1995 Preprint gr-qc/9504018)
27. Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T 1995 Quantization of diffeomorphism invariant theories of connections with local degrees of freedom J. Math. Phys. 36 6456-93 (Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T 1995 Preprint gr-qc/9504018)
28. Giulini D and Marolf D 1999 On the generality of refined algebraic quantization Class. Quantum Grav. 16 2479-88 Giulini D and Marolf D 1998 Preprint gr-qc/9812024
29. Giulini D and Marolf D 1999 On the generality of refined algebraic quantization Class. Quantum Grav. 16 2479-88 (Giulini D and Marolf D 1998 Preprint gr-qc/9812024
30. Landsman N 1995 Rieffel induction as generalized quantum Marsden-Weinstein reduction J. Geom. Phys. 15 285-319 Landsman N 1993 Preprint hep-th/9305088)
31. Landsman N 1995 Rieffel induction as generalized quantum Marsden-Weinstein reduction J. Geom. Phys. 15 285-319 (Landsman N 1993 Preprint hep-th/9305088)
32. Higuchi A 1991 Quantum linearization instabilities of de Sitter space-time 2 Class. Quantum Grav. 8 1983-2004
33. Marolf D 1995 Quantum observables and recollapsing dynamics Class. Quantum Grav. 12 1199-220 Marolf D 1994 Preprint gr-qc/9404053)
34. Marolf D 1995 Quantum observables and recollapsing dynamics Class. Quantum Grav. 12 1199-220 (Marolf D 1994 Preprint gr-qc/9404053)
35. Marolf D 1997 Refined algebraic quantization: systems with a single constraint Symplectic Singularities and Geometry of Gauge Fields (Warsaw: Banach) Marolf D 1997 Preprint gr-qc/9508015 (some corrections are present only in the version in the LANL archives))
36. Marolf D 1997 Refined algebraic quantization: systems with a single constraint Symplectic Singularities and Geometry of Gauge Fields (Warsaw: Banach) (Marolf D 1997 Preprint gr-qc/9508015 (some corrections are present only in the version in the LANL archives))
37. Kirillov A 1976 Elements of the Theory of Representations (New York: Springer)
38. Mackey G W 1963 Infinite-dimensional group representations Bull. Am. Math. Soc. 69 628-86
39. Dixmier J 1977 C*-Algebras (Amsterdam: North-Holland)
40. Marolf D 1995 The spectral analysis inner product for quantum gravity Proc. 7th Marcel-Grossman Conf. ed R Ruffini and M Keiser (Singapore: World Scientific) Marolf D 1994 Preprint gr-qc/9409036)
41. Marolf D 1995 The spectral analysis inner product for quantum gravity Proc. 7th Marcel-Grossman Conf. ed R Ruffini and M Keiser (Singapore: World Scientific) (Marolf D 1994 Preprint gr-qc/9409036)
42. Kelley J L 1955 General Topology (New York: Van Nostrand Reinhold)
43. Fell J M G 1960 The dual spaces of C*-algebras Trans. Am. Math. Soc. 94 365-403
44. 2 Class. Quantum Grav. 12 2735-46 Giulini D and Louko J 1995 Preprint gr-qc/9504035)
45. 2 Class. Quantum Grav. 12 2735-46 (Giulini D and Louko J 1995 Preprint gr-qc/9504035)
46. Carlip S and Nelson J 1999 The quantum modular group in (2 + 1 )-dimensional gravity Phys. Rev. D 59 024012 Carlip S and Nelson J 1998 Preprint gr-qc/9807087)
47. Carlip S and Nelson J 1999 The quantum modular group in (2 + 1 )-dimensional gravity Phys. Rev. D 59 024012 (Carlip S and Nelson J 1998 Preprint gr-qc/9807087)
48. Rieffel M A 1990 Proper actions of groups on C*-algebras Mappings of Operator Algebras ed H Araki and R V Kadison (Boston, MA: Birkhäuser) pp 141-82
49. Kuchǎr K 1986 Hamiltonian dynamics of gauge systems Phys. Rev. D 34 3031-43 Kuchǎr K 1986 Covariant factor ordering of gauge systems Phys. Rev. D 34 3044-57
50. Kuchǎr K 1986 Hamiltonian dynamics of gauge systems Phys. Rev. D 34 3031-43 Kuchǎr K 1986 Covariant factor ordering of gauge systems Phys. Rev. D 34 3044-57
51. Gomberoff A and Marolf D 1999 On group averaging for SO(n, 1 ) Preprint gr-qc/9902069
52. Abraham R and Marsden J E 1979 Foundations of Mechanics (Reading, MA: Benjamin-Cummings)
53. Arnold V I 1984 Mathematical Methods of Classical Mechanics (New York: Springer)
54. Guillemin V and Sternberg S 1984 Symplectic Techniques in Physics (Cambridge: Cambridge University Press)