Hilbert space built over connections with a non-compact structure group

Classical and Quantum Gravity

Volumn 22, Issue 7, 2005, Pages 1329-1359

  Okołów, Andrzej ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17044375029     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/22/7/009     Document Type: Article

References (23)

1. Freidel L and Livine E R 2003 Spin networks for non-compact groups J. Math. Phys. 44 1322-56 (Preprint hep-th/0205268)
2. Livine E R 2002 Projected spin networks for Lorentz connection: linking spin foams and loop gravity Class. Quantum Grav. 19 5525-42 (Preprint gr-qc/0207084)
3. 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 (Preprint gr-qc/9504018)
4. Ashtekar A 1986 New variables for classical and quantum gravity Phys. Rev. Lett. 57 2244 Ashtekar A 1987 A new Hamiltonian formulation of general relativity Phys. Rev. D 36 1587
5. Ashtekar A 1986 New variables for classical and quantum gravity Phys. Rev. Lett. 57 2244 Ashtekar A 1987 A new Hamiltonian formulation of general relativity Phys. Rev. D 36 1587
6. Immirzi G 1997 Quantum gravity and Regge calculus Nucl. Phys. Proc. Suppl. 57 65-72 (Preprint gr-qc/9701052)
7. Ashtekar A, Baez J and Krasnov K 2000 Quantum geometry of isolated horizons and black hole entropy Adv. Theor. Math. Phys. 4 1-94 (Preprint gr-qc/0005126)
8. Ashtekar A and Lewandowski L 2004 Background independent quantum gravity: a status report Class. Quantum Grav. 21 R53 (Preprint gr-qc/0404018) Thiemann T 2001 Introduction to modern canonical quantum general relativity Preprint gr-qc/0110034
9. Ashtekar A and Lewandowski L 2004 Background independent quantum gravity: a status report Class. Quantum Grav. 21 R53 (Preprint gr-qc/0404018) Thiemann T 2001 Introduction to modern canonical quantum general relativity Preprint gr-qc/0110034
10. Thiemann T 1998 Quantum spin dynamics (QSD) Class. Quantum Grav. 15 839-73 (Preprint gr-qc/9606089)
11. Lewandowski J 2001 private communication
12. Ashtekar A and Lewandowski J 1994 Representation theory of analytic holonomy C*-algebras Knots and Quantum Gravity ed J Baez (Oxford: Oxford University Press) (Preprint gr-qc/9311010)
13. Ashtekar A and Lewandowski J 1995 Projective techniques and functional integration for gauge theories J. Math. Phys. 36 2170-91 (Preprint gr-qc/9411046)
14. Ashtekar A and Lewandowski J 1997 Quantum theory of geometry: I. Area operators Class. Quantum Grav. 14 A55-82 (Preprint gr-qc/9602046)
15. Ashtekar A 2002 Notes on integration theory of spaces of connections with non-compact structure group (notes based on discussions with Fleischhack, Freidel, Lewandowski and Sahlmann) unpublished
16. Kobayashi S and Nomizu K 1963 Foundations of Differential Geometry (New York: Interscience)
17. Ashtekar A and Isham C J 1992 Representations of the holonomy algebras for gravity and non-Abelian gauge theories Class. Quantum Grav. 9 1433-67 (Preprint hep-th/9202053)
18. Ashtekar A, Corichi A and Zapata J A 1998 Quantum theory of geometry: III. Non-commutativity of Riemannian structures Class. Quantum Grav. 15 2955-72 (Preprint gr-qc/9806041)
19. Sahlmann H 2002 When do measures on the space of connections support the triad operators of loop quantum gravity? Preprint gr-qc/0207112 Sahlmann H and Thiemann T 2003 On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories Preprint gr-qc/0302090 Okołów A and Lewandowski J 2003 Diffeomorphism covariant representations of the holonomy-flux *-algebra Class. Quantum Grav. 20 3543-67 (Preprint gr-qc/0302059) Okołów A and Lewandowski J 2005 Automorphism covariant representations of the holonomy-flux *-algebra Class. Quantum Grav. 22 657-79 (Preprint gr-qc/0405119)
20. Sahlmann H 2002 When do measures on the space of connections support the triad operators of loop quantum gravity? Preprint gr-qc/0207112 Sahlmann H and Thiemann T 2003 On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories Preprint gr-qc/0302090 Okołów A and Lewandowski J 2003 Diffeomorphism covariant representations of the holonomy-flux *-algebra Class. Quantum Grav. 20 3543-67 (Preprint gr-qc/0302059) Okołów A and Lewandowski J 2005 Automorphism covariant representations of the holonomy-flux *-algebra Class. Quantum Grav. 22 657-79 (Preprint gr-qc/0405119)
21. Sahlmann H 2002 When do measures on the space of connections support the triad operators of loop quantum gravity? Preprint gr-qc/0207112 Sahlmann H and Thiemann T 2003 On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories Preprint gr-qc/0302090 Okołów A and Lewandowski J 2003 Diffeomorphism covariant representations of the holonomy-flux *-algebra Class. Quantum Grav. 20 3543-67 (Preprint gr-qc/0302059) Okołów A and Lewandowski J 2005 Automorphism covariant representations of the holonomy-flux *-algebra Class. Quantum Grav. 22 657-79 (Preprint gr-qc/0405119)
22. Sahlmann H 2002 When do measures on the space of connections support the triad operators of loop quantum gravity? Preprint gr-qc/0207112 Sahlmann H and Thiemann T 2003 On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories Preprint gr-qc/0302090 Okołów A and Lewandowski J 2003 Diffeomorphism covariant representations of the holonomy-flux *-algebra Class. Quantum Grav. 20 3543-67 (Preprint gr-qc/0302059) Okołów A and Lewandowski J 2005 Automorphism covariant representations of the holonomy-flux *-algebra Class. Quantum Grav. 22 657-79 (Preprint gr-qc/0405119)
23. Alexandrov S 2000 S O (4, ℂ)-covariant Ashtekar-Barbero gravity and the Immirzi parameter Class. Quantum Grav. 17 4255-68 (Preprint gr-qc/0005085)