Unboundedness of triad-like operators in loop quantum gravity

Classical and Quantum Gravity

Volumn 23, Issue 5, 2006, Pages 1429-1483

  Brunnemann, J ^a,b   Thiemann, T ^a,b  

^a ALBERT EINSTEIN INSTITUT   (Germany)

^b PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33244473054     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/23/5/002     Document Type: Article

References (28)

1. Brunnemann J and Thiemann T 2006 On (cosmological) singularity avoidance in loop quantum gravity Class. Quantum Grav. 23 1395-427 (Preprint gr-gc/0505032)
2. Rovelli C 2004 Quantum Gravity (Cambridge: Cambridge University Press)
3. Thiemann T 2006 Modern Canonical General Relativity (Cambridge: Cambridge University Press) (Preprint gr-qc/0110034)
4. Rovelli C 1998 Loop quantum gravity Living Rev. Rel. 1 1 (Preprint gr-qc/9710008)
5. Ashtekar A and Lewandowski J 2004 Background independent quantum gravity: a status report Class. Quantum Grav. 21 R53 (Preprint gr-qc/0404018)
6. Smolin L 2004 An invitation to loop quantum gravity Preprint hep-th/0408048
7. Thiemann T 2003 Lectures on Loop Quantum Gravity (Lecture Notes in Physics vol 631) (Berlin: Springer) pp 41-135 (Preprint gr-qc/0210094)
8. Bojowald M and Morales-Tecotl H 2004 Cosmological Applications of Loop Quantum Gravity (Lecture Notes in Physics vol 646) (Berlin: Springer) pp 421-62 (Preprint gr-qc/0306008)
9. Thiemann T 1996 Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity Phys. Lett. B 380 257-64 (Preprint gr-qc/9606088)
10. Thiemann T 1998 Quantum spin dynamics (QSD): I Class. Quantum Grav. 15 839-73 (Preprint gr-qc/9606089)
11. Thiemann T 1998 Quantum spin dynamics (QSD): II. The kernel of the Wheeler-DeWitt constraint operator Class. Quantum Grav. 15 875-905 (Preprint gr-qc/9606090)
12. Thiemann T 1998 Quantum spin dynamics (QSD): III. Quantum constraint algebra and physical scalar product in quantum general relativity Class. Quantum Grav. 15 1207-47 (Preprint gr-qc/9705017)
13. Thiemann T 1998 Quantum spin dynamics (QSD): IV. 2+1 Euclidean quantum gravity as a model to test 3+1 Lorentzian quantum gravity Class. Quantum Grav. 15 1249-80 (Preprint gr-qc/9705018)
14. Thiemann T 1998 Quantum spin dynamics (QSD): V. Quantum gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories Class. Quantum Grav. 15 1281-314 (Preprint gr-qc/9705019)
15. Thiemann T 1998 A length operator for canonical quantum gravity J. Math. Phys. 39 3372-92 (Preprint gr-qc/9606092)
16. Thiemann T 2002 Complexifier coherent states for canonical quantum general relativity Preprint gr-qc/0206037
17. Brunnemann J and Thiemann T 2004 Simplification of the spectral analysis of the volume operator in loop quantum gravity Preprint gr-qc/0405060
18. Thiemann T 1998 Closed formula for the matrix elements of the volume operator in canonical quantum gravity J. Math. Phys. 39 3347-71 (Preprint gr-qc/9606091)
19. De Pietri R 1997 Spin networks and recoupling in loop quantum gravity Preprint gr-qc/9701041
20. Thiemann T 1998 Kinematical Hilbert spaces for fermionic and Higgs quantum field theories Class. Quantum Grav. 15 1487 (Preprint gr-qc/9705021)
21. Edmonds A R 1996 Angular Momentum in Quantum Mechanics 4th edn (Princeton, NJ: Princeton University Press)
22. Sexl R U and Urbantke H K 2001 Relativity, Groups, Particles (Vienna: Springer)
23. Brunnemann J 2002 Spectral analysis of the volume operator in canonical quantum general relativity Diploma Thesis Humboldt University Berlin
24. Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): II. Peakedness properties Class. Quantum Grav. 18 2561-636 (Preprint hep-th/0005237)
25. Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): III. Ehrenfest theorems Class. Quantum Grav. 18 4629-81 (Preprint hep-th/0005234)
26. Sahlmann H and Thiemann T 2006 Towards the QFT on curved spacetime limit of QGR: I. A general scheme Class. Quantum Grav. 23 867-908 (Preprint gr-qc/0207030)
27. Sahlmann H and Thiemann T 2006 Towards the QFT on curved spacetime limit of QGR: II. A concrete implementation Class. Quantum Grav. 23 909-54 (Preprint gr-qc/0207031)
28. Bochner S 1948 Vorlesungen über Fouriersche Integrale (New York: Chelsea)