Group averaging, positive definiteness and superselection sectors

Journal of Physics: Conference Series

Volumn 33, Issue 1, 2006, Pages 142-149

  Louko, Jorma ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33645675838     PISSN: 17426588     EISSN: 17426596     Source Type: Conference Proceeding    
DOI: 10.1088/1742-6596/33/1/013     Document Type: Article

References (38)

1. Higuchi A 1991 Quantum linearization instabilities of de Sitter space-time 2 Class. Quantum Grav 8 1983-2004
2. Landsman N P 1995 Rieffel induction as generalized quantum Marsden-Weinstein reduction J. Geom. Phys 15 285-319 Preprint hep-th/9305088
3. Landsman N P 1998 The quantization of constrained systems: from symplectic reduction to Rieffel induction Quantization, Coherent States and Poisson Structures: Proc. of the XIV Workshop on Geometric Methods in Physics (Biaowiea 1995) ed A Strasburger et al (Warsaw: Polish Scientific Publishers) p 73-89 Preprint gr-qc/9508015
4. Landsman N P 1995 Against the Wheeler-DeWitt equation Class. Quantum Grav. 12 119-123 Preprint gr-qc/9510033
5. Landsman N P and Wren K K 1997 Constrained quantization and θ-angles Nucl. Phys. B 502 537-560 Preprint hep-th/9706178
6. Marolf D 1995 Quantum observables and recollapsing dynamics Class. Quantum Grav 12 1199-1220 Preprint gr-qc/9404053
7. Ashtekar A, Lewandowski J, Marolf D, Mouro J and Thiemann T 1995 Quantization of diffeomorphism invariant theories of connections with local degrees of freedom J. Math. Phys. 36 6456-6493 Preprint gr-qc/9504018
8. Marolf D 1997 Refined algebraic quantization: Systems with a single constraint Symplectic Singularities and Geometry of Gauge Fields (Warsaw: Banach Center Publications, Polish Academy of Sciences, Institute of Mathematics) Preprint gr-qc/9508015
9. Giulini D and Marolf D 1999 On the generality of Refined algebraic quantization Class. Quantum Grav 16 2479-2488 Preprint gr-qc/9812024
10. Giulini D and Marolf D 1999 A uniqueness theorem for constraint quantization Class. Quantum Grav 16 2489-2505 Preprint gr-qc/9902045
11. Gombero A and Marolf D 1999 On group averaging for SO(n, 1) Int. J. Mod. Phys. D 8 8-519 Preprint gr-qc/9902069
12. Louko J and Rovelli C 2000 Refined algebraic quantization in the oscillator representation of SL(2, ) J. Math. Phys 41 132-155 Preprint gr-qc/9907004
13. Louko J and Molgado A 2004 Group averaging in the, (p, q), oscillator representation of SL(2, ) J. Math. Phys 45 1919-1943 Preprint gr-qc/0312014
14. Louko J and Molgado A 2005 Refined algebraic quantisation with the triangular subgroup of SL(2, ) Int. J. Mod. Phys. D 14 1131-1157 Preprint gr-qc/0404100
15. Louko J and Molgado A 2005 Superselection sectors in the Ashtekar-Horowitz-Boulware model Class. Quantum Grav 22 4007-4019 Preprint gr-qc/0505097
16. Giulini D 2000 Group averaging and Refined algebraic quantization Nucl. Phys. Proc. Suppl 88 385-388 Preprint gr-qc/0003040
17. Marolf D 2002 Group averaging and Refined algebraic quantization: Where are we now? The Ninth Marcel Grossmann meeting: Proc., (Rome 2000) ed V G Gurzadyan, R T Jantzen and R Ruffni (Singapore: World Scientific) Preprint gr-qc/0011112
18. Noui K and Perez A 2005 Three-dimensional loop quantum gravity: Physical scalar product and spin foam models Class. Quantum Grav. 22 1739-1762 Preprint gr-qc/0402110
19. Shvedov O Yu 2002 On correspondence of BRST-BFV, Dirac and Refined algebraic quantisations of constrained systems Ann. Phys., (N.Y.) 302 2-21 Preprint hep-th/0111270
20. Klauder J R 1997 Coherent state quantization of constraint systems Ann. Phys. (N.Y.) 254 419-453 Preprint quant-ph/9604033
21. Thiemann T 2003 The Phoenix Project: Master constraint program for loop quantum gravity Preprint gr-qc/0305080
22. Dittrich B and Thiemann T 2004 Testing the master constraint program for loop quantum gravity. I. General framework Preprint gr-qc/0411138
23. Spark N T 2003 The fastest man on Earth Ann. Improb. Res. 9 (5) 4-24 Website http://www.improb.com/airchives/paperair/
24. Montesinos M, Rovelli C and Thiemann T 1999 SL(2, ) model with two Hamiltonian constraints Phys. Rev. D 60 044009 Preprint gr-qc/9901073
25. Henneaux M and Teitelboim C 1992 Quantization of Gauge Systems (Princeton: Princeton University)
26. Kuchar K V 1992 Time and interpretations of quantum gravity Proc. 4th Canadian Conf. on General Relativity and Relativistic Astrophysics, (Winnipeg 1991) ed G Kunstatter, D E Vincent and J G Williams (Singapore: World Scientific) p 211-314
27. Howe R and Tan E C 1992 Non-Abelian Harmonic Analysis: Applications of SL(2, ) (New York: Springer)
28. Tuynman G M 1990 Reduction, quantization, and nonunimodular groups J. Math. Phys 31 83-90
29. Duval C, Elhadad J, Gotay M J and Tuynman G M 1990 Nonunimodularity and the quantization of the pseudorigid body Hamiltonian Systems, Transformation Groups and Spectral Transform Methods ed J Harnad and J Marsden (Montreal: Les Publications du CRM) p 149-160
30. Duval C, Elhadad J, Gotay M J, Śniatycki J and Tuynman G M 1991 Quantization and bosonic BRST theory Ann. Phys. (N.Y.) 206 1-26
31. Vilenkin N Ja and Klimyk A V 1993 Representation of Lie Groups and Special Functions vol 2 (Dordrecht: Kluwer Academic)
32. Boulware D G 1983 Comment on On the canonical approach to quantum gravity Phys. Rev. D 28 414-416
33. Ashtekar A and Horowitz G T 1982 On the canonical approach to quantum gravity Phys. Rev. D 26 3342-3353
34. Gotay M J 1986 Negative energy states in quantum gravity? Class. Quantum Grav 3 487-491
35. Tate R S 1992 An Algebraic Approach to the Quantization of Constrained Systems: Finite Dimensional Examples PhD dissertation (Syracuse University) Preprint gr-qc/9304043
36. Ashtekar A and Tate R S 1994 An algebraic extension of Dirac quantization: Examples J. Math. Phys 35 6434-6470 Preprint gr-qc/9405073
37. Woodhouse N M J 1992 Geometric Quantization 2nd ed (Oxford: Clarendon)
38. Śniatycki J 1980 Geometric Quantization and Quantum Mechanics (New York: Springer)