Gauge-invariant coherent states for loop quantum gravity: II. non-abelian gauge groups

Classical and Quantum Gravity

Volumn 26, Issue 4, 2009, Pages

  Bahr, Benjamin ^a   Thiemann, Thomas ^a,b  

^a ALBERT EINSTEIN INSTITUT   (Germany)

^b PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 68949163940     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/26/4/045012     Document Type: Article

References (28)

1. Bahr B and Thiemann T 2009 Gauge-invariant coherent states for loop quantum gravity: I. Abelian gauge groups Class. Quantum Grav. 26 045011 (arXiv:0709.4619)
2. Thiemann T 2001 Gauge field theory coherent states (GCS): I. General properties Class. Quantum Grav. 18 2025 (arXiv:hep-th/0005233)
3. Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): II. Peakedness properties Class. Quantum Grav. 18 2561 (arXiv:hep-th/0005237)
4. Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): III. Ehrenfest theorems Class. Quantum Grav. 18 4629 (arXiv:hep-th/0005234)
5. Thiemann T 2006 Introduction to Modern Canonical Quantum General Relativity (Cambridge Monographs on Mathematical Physics) (Cambridge: Cambridge University Press)
6. Rovelli C 2004 Quantum gravity Cambridge Monographs on Mathematical Physics (Cambridge: Cambridge University Press)
7. Smolin L 2004 An invitation to loop quantum gravity, in Quantum Theory and Symmetries: Proc. 3rd Int. Symp. (Cincinnati, OH, 10-14 Sept 2003) ed P C Argyres, T J Hodges, F Mansouri, J J Scanio, P Suranyi and L C R Wijewardhana (Singapore: World Scientific) pp 655-82 (arXiv:hep-th/0408048)
8. Ashtekar A, Lewandowski J, Marolf D, Mourao J and Thiemann T 1995 Quantization of diffeomorphism invariant theories of connections with local degrees of freedom J. Math. Phys. 36 6456 (arXiv:gr-qc/9504018)
9. Lewandowski J, Okołow A, Sahlmann H and Thiemann T 2006 Uniqueness of diffeomorphism invariant states on holonomy-flux algebras Commun. Math. Phys. 267 703 (arXiv:gr-qc/0504147)
10. Rovelli C and Smolin L 1995 Spin networks and quantum gravity Phys. Rev. D 52 5743 (arXiv:gr-qc/9505006)
11. Hall B 1994 The Segal-Bargmann 'coherent state' transform for compact Lie groups J. Funct. Anal. 122 103
12. Hall B 1997 The inverse Segal-Bargmann transform for compact Lie groups J. Funct. Anal. 143 98
13. Hall B 1997 Phase space bounds for quantum mechanics on a compact Lie group Commun. Math. Phys. 184 233
14. Giesel K and Thiemann T 2007 Algebraic quantum gravity (AQG): I. Conceptual setup Class. Quantum Grav. 24 2465 (arXiv:gr-qc/0607099)
15. Giesel K and Thiemann T 2007 Algebraic quantum gravity (AQG): II. Semiclassical analysis Class. Quantum Grav. 24 2499 (arXiv:gr-qc/0607100)
16. Giesel K and Thiemann T 2007 Algebraic quantum gravity (AQG): III. Semiclassical perturbation theory Class. Quantum Grav. 24 2565 (arXiv:gr-qc/0607101)
17. Flori C and Thiemann T Semiclassical analysis of the loop quantum gravity volume operator utilising cylindrically consistent complexifier coherent states (in preparation)
18. Livine E R and Speziale S 2007 A new spinfoam vertex for quantum gravity Phys. Rev. D 76 084028 (arXiv:0705.0674)
19. Livine E R and Speziale S 2008 Consistently solving the simplicity constraints for spinfoam quantum gravity Europhys. Lett. 81 50004 (arXiv:0708.1915)
20. Freidel L and Krasnov K 2008 A new spin foam model for 4d gravity Class. Quantum Grav. 25 125018 (arXiv:0708.1595)
21. N. Biggs 1993 Algebraic Graph Theory 2nd edn (Cambridge: Cambridge Mathematical Library)
22. Freidel L and Livine E 2003 Spin networks for non-compact groups J. Math. Phys. 44 1322 (arXiv:hep-th/0205268)
23. Thiemann T 2001 Complexifier coherent states for quantum general relativity Class. Quantum Grav. 18 2025 (arXiv:gr-qc/0206037)
24. Thiemann T 2006 The Phoenix Project: master constraint programme for loop quantum gravity Class. Quantum Grav. 23 2211 (arXiv:gr-qc/0305080)
25. Thiemann T 2006 Quantum spin dynamics: VIII. The master constraint Class. Quantum Grav. 23 2249 (arXiv:gr-qc/0510011)
26. Baez J, Christensen D and Egan G 2002 Asymptotics of 10j symbols Class. Quantum Grav. 19 6489-513 (arXiv:gr-qc/0208010) (Pubitemid 37026802)
27. Barrett J W and Steele C M 2003 Asymptotics of relativistic spin networks Class. Quantum Grav. 20 1341-62 (arXiv:gr-qc/0209023)
28. Freidel L and Louapre D 2003 Asymptotics of 6j and 10j symbols Class. Quantum Grav. 20 1267-94 (arXiv:hep-th/0209134)