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G. Papageorgiou and B.J. Schroers JHEP11(2009)009 doi:10.1088/1126-6708/2009/11/009

A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions

G. Papageorgiou and B.J. Schroers

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[1]
J. Christian, 1997 Exactly soluble sector of quantum gravity, Phy. Rev. D 56 4844 [gr-qc/9701013]
CrossRef  Preprint  SPIRES 
[2]
S. Carlip, 1998 Quantum gravity in 2+1 dimensions, Cambridge University Press, Cambridge U.K.
CrossRef 
[3]
D.R. Grigore, 1996 The projective unitary irreducible representations of the Galilei group in (1+2)-dimensions, J. Math. Phys. 37 460 [hep-th/9312048]
CrossRef  Preprint  SPIRES 
[4]
J. Mund and R. Schrader, Hilbert spaces for nonrelativistic and relativistic 'Free' Plektons (Particles with braid group statistics), [hep-th/9310054]
Preprint  SPIRES 
[5]
Y. Brihaye, C. Gonera, S. Giller and P. Kosinski, Galilean invariance in (2+1)-dimensions, [hep-th/9503046]
Preprint  SPIRES 
[6]
J.M. Lévy-Leblond, 1971 Galilei group and Galilean invariance, E. Loebl ed., Group Theory and Applications Vol II, Academic Press, New York U.S.A.

[7]
S.K. Bose, 1995 The Galilean group in 2+1 space-times and its central extension, Commun. Math. Phys. 169 385
CrossRef 
[8]
A. Ballesteros, M. Gadella and M.A. Del Olmo, 1992 Moyal quantisation of 2+1 dimensional Galilean systems J. Math. Phys. 33 3379
CrossRef 
[9]
J. Lukierski, P.C. Stichel and W.J. Zakrzewski, 1997 Galilean invariant (2+1)-dimensional models with a Chern-Simons-like term and D = 2 noncommutative geometry, Annals Phys. 260 224 [hep-th/9612017]
CrossRef  Preprint  SPIRES 
[10]
C. Duval and P.A. Horvathy, 2000 The 'Peierls substitution' and the exotic Galilei group, Phys. Lett. B 479 284 [hep-th/0002233]
CrossRef  Preprint  SPIRES 
[11]
P.A. Horvathy and M.S. Plyushchay, 2002 Nonrelativistic anyons and exotic Galilean symmetry J. High Energy Phys. JHEP06(2002)033 [hep-th/0201228]
IOPscience  Preprint  SPIRES 
[12]
P.A. Horvathy and M.S. Plyushchay, 2004 Anyon wave equations and the noncommutative plane, Phys. Lett. B 595 547 [hep-th/0404137]
CrossRef  Preprint  SPIRES 
[13]
R. Jackiw, and V.P. Nair, 2000 Anyon spin and the exotic central extension of the planar Galilei group, Phys. Lett. B 480 237 [hep-th/0003130]
CrossRef  Preprint  SPIRES 
[14]
R. Jackiw, and V.P. Nair, 2003 Remarks on the exotic central extension of the planar Galilei group, Phys. Lett. B 551 166 [hep-th/0211119]
CrossRef  Preprint  SPIRES 
[15]
J. Negro, M.A. del Olmo and J. Tosiek, 2006 Anyons, group theory and planar physics, J. Math. Phys. 47 033508 [math-ph/0512007]
CrossRef  Preprint  SPIRES 
[16]
C. Duval and P.A. Horvathy, 2002 Spin and exotic Galilean symmetry, Phys. Lett. B 547 306 [Erratum ibid B 588 (2004) 228] [hep-th/0209166]
CrossRef  Preprint  SPIRES 
[17]
C.R. Hagen, 2002 Second central extension in Galilean covariant field theory, Phys. Lett. B 539 168 [quant-ph/0203109]
CrossRef  Preprint  SPIRES 
[18]
H. Bacry and J. Levy-Leblond, 1968 Possible kinematics, J. Math. Phys. 9 1605
CrossRef 
[19]
F.J. Herranz and M. Santander, 2+1 kinematical expansions: from Galilei to de Sitter algebras, [math-ph/9902006]
Preprint 
[20]
D. Cangemi and R. Jackiw, 1992 Gauge invariant formulations of lineal gravity, Phys. Rev. Lett. 69 233 [hep-th/9203056]
CrossRef  Preprint  PubMed  SPIRES 
[21]
C.R. Nappi and E. Witten, 1993 A WZW model based on a nonsemisimple group, Phys. Rev. Lett. 71 3751 [hep-th/9310112]
CrossRef  Preprint  PubMed  SPIRES 
[22]
J.M. Figueroa-O'Farrill and S. Stanciu, 2000 More D-branes in the Nappi-Witten background J. High Energy Phys. JHEP01(2000)024 [hep-th/9909164]
IOPscience  Preprint  SPIRES 
[23]
V.V. Fock and A.A. Rosly, 1999 Poisson structures on moduli of flat connections on Riemann surfaces and r-matrices, Am. Math. Soc. Transl. 191 67 [math/9802054]
Preprint  SPIRES 
[24]
A.Y. Alekseev, H. Grosse and V. Schomerus, 1995 Combinatorial quantization of the Hamiltonian Chern-Simons theory, Commun. Math. Phys. 172 317 [hep-th/9403066]
CrossRef  Preprint  SPIRES 
[25]
A.Y. Alekseev, H. Grosse and V. Schomerus, 1995 Combinatorial quantization of the Hamiltonian Chern-Simons theory. 2, Commun. Math. Phys. 174 561 [hep-th/9408097]
CrossRef  Preprint  SPIRES 
[26]
A.Yu. Alekseev and V. Schomerus, 1996 Representation theory of Chern-Simons observables Duke Math. J. 85 447 [q-alg/9503016]
CrossRef  Preprint  SPIRES 
[27]
B.J. Schroers, 2001 Combinatorial quantisation of Euclidean gravity in three dimensions, in N.P. Landsman, M. Pflaum, M. Schlichenmaier eds., Birkhäuser, Quantization of singular symplectic quotients Prog. Math. 198 307 [math/0006228]
Preprint  SPIRES 
[28]
E. Buffenoir, K. Noui and P. Roche, 2002 Hamiltonian quantization of Chern-Simons theory with SL(2,C) group, Class. Quant. Grav. 19 4953 [hep-th/0202121]
IOPscience  Preprint  SPIRES 
[29]
F.A. Bais, N.M. Muller and B.J. Schroers, 2002 Quantum group symmetry and particle scattering in (2+1)- dimensional quantum gravity, Nucl. Phys. B 640 3 [hep-th/0205021]
CrossRef  Preprint  SPIRES 
[30]
C. Meusburger and B.J. Schroers, 2003 Poisson structure and symmetry in the Chern-Simons formulation of (2+1)-dimensional gravity, Class. Quant. Grav. 20 2193 [gr-qc/0301108]
IOPscience  Preprint  SPIRES 
[31]
C. Meusburger and B.J. Schroers, 2004 The quantisation of Poisson structures arising in Chern-Simons theory with gauge group G ⋉ &frakg;*, Adv. Theor. Math. Phys. 7 1003 [hep-th/0310218]
Preprint  SPIRES 
[32]
S.P. Martin, 1989 Observables in 2+1 dimensional gravity, Nucl. Phys. B 327 178
CrossRef 
[33]
C. Meusburger, 2007 Geometrical (2+1)-gravity and the Chern-Simons formulation: Grafting, Dehn twists, Wilson loop observables and the cosmological constant, Commun. Math. Phys. 273 705 [gr-qc/0607121]
CrossRef  Preprint  SPIRES 
[34]
C. Meusburger and B.J. Schroers, 2008 Quaternionic and Poisson-Lie structures in 3 D gravity: the cosmological constant as deformation parameter, J. Math. Phys. 49 083510 [0708.1507]
CrossRef  Preprint  SPIRES 
[35]
V.I. Arnold, 1989 Mathematical methods of classical mechanics, Springer Verlag, New York U.S.A.

[36]
A.A. Kirillov, 1976 Elements of the theory of representations, Grundlehren der mathematischen Wissenschaft 220, Springer Verlag, Berlin Germany

[37]
A. Achucarro and P. Townsend, 1986 A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories, Phys. Lett. B 180 89
CrossRef 
[38]
E. Witten, 1988 (2+1)-dimensional gravity as an exactly soluble system, Nucl. Phys. B 311 46
CrossRef 
[39]
S. Deser, R. Jackiw and G. 't Hooft, 1984 Three-dimensional Einstein gravity: dynamics of flat space, Ann. Phys. 152 220
CrossRef 
[40]
P. de Sousa Gerbert, 1990 On spin and (quantum) gravity in (2+1)-dimensions, Nucl. Phys. B 346 440
CrossRef 
[41]
C. Meusburger and B.J. Schroers, 2005 Boundary conditions and symplectic structure in the Chern-Simons formulation of (2+1)-dimensional gravity, Class. Quant. Grav. 22 3689 [gr-qc/0505071]
IOPscience  Preprint  SPIRES 
[42]
H.-J. Matschull, 1999 On the relation between 2+1 Einstein gravity and Chern-Simons theory, Class. Quant. Grav. 16 2599 [gr-qc/9903040]
IOPscience  Preprint  SPIRES 
[43]
C. Meusburger and B.J. Schroers, 2006 Phase space structure of Chern-Simons theory with a non- standard puncture, Nucl. Phys. B 738 425 [hep-th/0505143]
CrossRef  Preprint  SPIRES 
[44]
G. 't Hooft, 1996 Quantization of point particles in 2+1 dimensional gravity and space-time discreteness, Class. Quant. Grav. 13 1023 [gr-qc/9601014]
IOPscience  Preprint  SPIRES 
[45]
H.-J. Matschull and M. Welling, 1998 Quantum mechanics of a point particle in 2+1 dimensional gravity, Class. Quant. Grav. 15 2981 [gr-qc/9708054]
IOPscience  Preprint  SPIRES 
[46]
M. Atiyah and R. Bott, 1982 Yang-Mills equations over Riemann surfaces Philos. T. R. Soc. Lond. 308 523
CrossRef 
[47]
M. Atiyah, 1990 The geometry and physics of knots, Cambridge University Press, Cambridge U.K.
CrossRef 
[48]
B.J. Schroers, Lessons from (2+1)-dimensional quantum gravity, PoS(QG-PH)035 [0710.5844]
Preprint  SPIRES 
[49]
A.Y. Alekseev and A.Z. Malkin, 1995 Symplectic structure of the moduli space of flat connection on a Riemann surface, Commun. Math. Phys. 169 99 [hep-th/9312004]
CrossRef  Preprint  SPIRES 
[50]
V. Chari and A. Pressley, 1994 Quantum groups, Cambridge University Press, Cambridge U.K.

[51]
G.W. Mackey, 1949 Imprimitivity for representations of locally compact groups. I, http://www.pnas.org/content/35/9/537.full.pdf+html Proc. Nat. Acad. Sci. U.S.A. 35 537
CrossRef 
[52]
A.O. Barut and R. Raczka, 1986 Theory of group representations and applications, World Scientific, Singapore

[53]
E. Kiritsis and C. Kounnas, 1994 String propagation in gravitational wave backgrounds, Phys. Lett. B 320 264 [Addendum ibid B 325 (1994) 536] [hep-th/9310202]
CrossRef  Preprint  SPIRES 
[54]
T. Koornwinder and N. Muller, 1997 The quantum double of a (locally) compact group J. Lie Theory 7 101 [q-alg/9605044]
Preprint  SPIRES 
[55]
F.A. Bais and N.M. Muller, 1998 Topological field theory and the quantum double of SU(2), Nucl. Phys. B 530 349 [hep-th/9804130]
CrossRef  Preprint  SPIRES 
[56]
F.A. Bais, P. van Driel and M. de Wild Propitius, 1992 Quantum symmetries in discrete gauge theories, Phys. Lett. B 280 63 [hep-th/9203046]
CrossRef  Preprint  SPIRES 
[57]
T.H. Koornwinder, F.A. Bais and N.M. Muller, 1998 Tensor product representations of the quantum double of a compact group, Commun. Math. Phys. 198 157 [q-alg/9712042]
CrossRef  Preprint  SPIRES 
[58]
I. Gott, J. Richard, 1991 Closed timelike curves produced by pairs of moving cosmic strings: exact solutions, Phys. Rev. Lett. 66 1126
CrossRef  PubMed 
[59]
C. Meusburger and B.J. Schroers, 2005 Mapping class group actions in Chern-Simons theory with gauge group G ⋉ &frakg;*, Nucl. Phys. B 706 569 [hep-th/0312049]
CrossRef  Preprint  SPIRES 
[60]
G. 't Hooft, 1988 Nonperturbative two particle scattering amplitudes in (2+1)-dimensional quantum gravity, Commun. Math. Phys. 117 685
CrossRef 
[61]
S. Deser and R. Jackiw, 1988 Classical and quantum scattering on a cone, Commun. Math. Phys. 118 495
CrossRef 
[62]
E. Batista and S. Majid, 2003 Noncommutative geometry of angular momentum space U(&fraks;&fraku;(2)), J. Math. Phys. 44 107 [hep-th/0205128]
CrossRef  Preprint  SPIRES 
[63]
L. Freidel and S. Majid, 2008 Noncommutative harmonic analysis, sampling theory and the Duflo Map in 2+1 quantum gravity, Class. Quant. Grav. 25 045006 [hep-th/0601004]
IOPscience  Preprint  SPIRES 
[64]
S. Majid and B.J. Schroers, 2009 q-Deformation and semidualisation in 3d quantum gravity, J. Phys. A 42 425402 [0806.2587]
IOPscience  Preprint  SPIRES 
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