Hamiltonian quantization of Chern-Simons theory with SL(2, ℂ) group

Classical and Quantum Gravity

Volumn 19, Issue 19, 2002, Pages 4953-5015

  Buffenoir, E ^a   Noui, K ^a   Roche, Ph ^a  

^a UNIV MONTPELLIER   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041428064     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/19/19/313     Document Type: Article

References (29)

1. Achucarro A and Townsend P K 1986 A Chem-Simons action for three-dimensional anti-de Sitter supergravity theories Phys. Lett. B 180 89-92
2. Alekseev A Yu, Grosse H and Schomerus V 1995 Combinatorial quantization of the Hamiltonian Chern-Simons theory: I Commun. Math. Phys. 172 317-58 (Preprint hep-th/9403066)
3. Alekseev A Yu, Grosse H and Schomerus V 1995 Combinatorial quantization of the Hamiltonian Chern-Simons theory: II Commun. Math. Phys. 174 561-604 (Preprint hep-th/9408097)
4. Alekseev A Yu and Schomerus V 1995 Representation theory of Chem-Simons observables Preprint q-alg/9503016
5. Alekseev A Yu 1995 Integrability in the Hamiltonian Chern-Simons theory St. Petersburg Math. J. 6 2 (Preprint hep-th/9311074)
6. Alekseev A Yu and Malkin A Z 1995 Symplectic structure of the moduli space of flat connections on a Riemann surface Commun. Math. Phys. 166 99-120 (Preprint hep-th/9312004)
7. 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 (Preprint gr-qc/ 9504018)
8. Atiyah M 1990 The Geometry and Physics of Knots (Cambridge: Cambridge University Press)
9. Balasubramanian V, de Boer J and Minic D 2001 Mass, entropy and holography in asymptotically de Sitter spaces Preprint hep-th/0110108
10. Buffenoir E and Roche Ph 1995 Two-dimensional lattice gauge theory based on a quantum group Commun. Math. Phys. 170 669-98 (Preprint hep-th/9405126)
11. Buffenoir E and Roche Ph 1996 Link invariants and combinatorial quantization of Hamiltonian Chern-Simons theory Commun. Math. Phys. 181 331-65 (Preprint q-alg/9507001)
12. Buffenoir E and Roche Ph 1999 Harmonic analysis on the quantum Lorentz group Commun. Math. Phys. 207 499-555
13. Buffenoir E and Roche Ph 1997 Harmonic analysis on the quantum Lorentz group Preprint q-alg/9710022
14. Buffenoir E and Roche Ph 2000 Tensor product of principal unitary representations of quantum Lorentz group and Askey-Wilson polynomials J. Math. Phys. 41 7715-51 (Preprint math.qa/9910147)
15. Carlip S 1998 Quantum Gravity in 2 + 1 Dimensions (Cambridge Monographs on Mathematical Physics) (Cambridge: Cambridge University Press)
16. Chari V and Preslley A 1995 A Guide to Quantum Groups (Cambridge: Cambridge University Press)
17. Ezawa K 1994 Classical and quantum evolution of the de Sitter and the anti-de Sitter universes in (2 + 1)-dimensions Phys. Rev. D 49 5211-26
18. Fock V V and Rosly A A 1998 Poisson structure on moduli of flat connections on Riemann surfaces and r-matrix Preprint math.QA/9802054
19. Goldman W 1984 The symplectic nature of fundamental groups of surfaces Adv. Math. 54 200-25
20. Matschull H-J 1999 On the relation between 2 + 1 Einstein gravity and Chem-Simons theory Class. Quantum Grav. 16 2599-609 (Preprint gr-qc/9903040)
21. Nelson J E and Regge T 1989 Homotopy groups and 2 + 1 quantum gravity Nucl. Phys. B 328 190-202
22. Nelson J E and Regge T 1994 Quantization of 2 + 1 gravity for genus 2 Phys. Rev. D 50 5125-9 (Preprint gr-qc/9311029)
23. Park M I 1998 Statistical entropy of three-dimensional Kerr-de Sitter space Phys. Lett. B 440 275 (Preprint hep-th/9806119)
24. Podles P and Woronowicz S L 1990 Quantum deformation of the Lorentz group Commun. Math. Phys. 130 381-431
25. Pusz W 1993 Irreducible unitary representations of quantum Lorentz group Commun. Math. Phys. 152 591-626
26. Turaev V 1994 Algebras of loops on surfaces, algebras of knots, and quantization Braid Group, Knot Theory and Statistical Mechanics II (Adv. Ser. Math. Phys. 17) (River Edge, NJ: World Science) pp 324-60
27. Van Daele A 1994 Multiplier Hopf algebras Trans. Am. Math. Soc. 342 917-32
28. Witten E 1988 (2 + 1)-dimensional gravity as an exactly soluble system Nucl. Phys. B 311 46-78
29. Witten E 1991 Quantization of Chern-Simons gauge theory with complex gauge group Commun. Math. Phys. 137 29-66