Fetching the paper…
Reading the bibliography…
By applying loop quantum gravity techniques to 3D gravity with a positive cosmological constant $\Lambda$, we show how the local gauge symmetry of the theory, encoded in the constraint algebra, acquires the quantum group structure of $so_q(4)$, with $ q = \exp{(i\hbar \sqrt{\Lambda}/2\kappa)}$.
E. Inonu and E. P. Wigner, “On the Contraction of groups and their represenations,” Proc. Nat. Acad. Sci. 39
1953
Earlier work this paper cites.
S. Alexandrov, M. Geiller and K. Noui, “Spin Foams and Canonical Quantization,” SIGMA 8
1961
Earlier work this paper cites.
S. Deser, R. Jackiw and G. ’t Hooft, “Three-Dimensional Einstein Gravity: Dynamics of Flat Space,” Annals Phys. 152
S. Deser and R. Jackiw, “Three-Dimensional Cosmological Gravity: Dynamics of Constant Curvature,” Annals Phys. 153 · 1984
Earlier work this paper cites.
E. Witten, “Quantum field theory and the Jones polynomial,” Commun. Math. Phys. 121
E. Witten, “(2+1)-Dimensional Gravity as an Exactly Soluble System,” Nucl. Phys. B 311 · 1989
Earlier work this paper cites.
P. de Sousa Gerbert, “On spin and (quantum) gravity in (2+1)-dimensions,” Nucl. Phys. B 346
1990
Earlier work this paper cites.
J. Lukierski, H. Ruegg, A. Nowicki and V. N. Tolstoi, “Q deformation of Poincare algebra,” Phys. Lett. B 264
1991
Earlier work this paper cites.
J. Lukierski, A. Nowicki and H. Ruegg, “Real forms of complex quantum anti-De Sitter algebra U-q(Sp(4:C)) and their contraction schemes,” Phys. Lett. B 271
1991
Earlier work this paper cites.
E. Celeghini, R. Giachetti, E. Sorace and M. Tarlini, “The Three-dimensional Euclidean quantum group E(3)-q and its R matrix,” J. Math. Phys. 32
1991
Earlier work this paper cites.
L. H. Kauffman, “Knots and physics,” Singapore, Singapore: World Scientific (1991) 538 p. (Series on knots and everything, 1)
L.H. Kauffman and S. Lins, “Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds,” Annals of Mathematical Studies, Princeton Univ. Press · 1991
Earlier work this paper cites.
J. Lukierski, A. Nowicki and H. Ruegg, “New quantum Poincare algebra and k deformed field theory,” Phys. Lett. B 293
1992
Earlier work this paper cites.
V. G. Turaev and O. Y. Viro, “State sum invariants of 3 manifolds and quantum 6j symbols,” Topology 31
1992
Earlier work this paper cites.
S. Majid and H. Ruegg, “Bicrossproduct structure of kappa Poincare group and noncommutative geometry,” Phys. Lett. B 334
1994
Earlier work this paper cites.
V. Chari and A. Pressley, “A guide to quantum groups,” Cambridge, UK: Univ. Pr. (1994) 651 p
1994
Earlier work this paper cites.
A. Ashtekar and J. Lewandowski, “Differential geometry on the space of connections via graphs and projective limits,” J. Geom. Phys. 17
A. Ashtekar and J. Lewandowski, “Projective techniques and functional integration for gauge theories,” J. Math. Phys. 36 · 1995
Cited alongside, same era.
S. Majid, “Foundations of Quantum Groups”, Cambridge Univ. Press, 1995
1995
Cited alongside, same era.
H. J. Matschull and M. Welling, “Quantum mechanics of a point particle in (2+1)-dimensional gravity,” Class. Quant. Grav. 15
1998
Cited alongside, same era.
F. A. Bais, N. M. Muller and B. J. Schroers, “Quantum group symmetry and particle scattering in (2+1)-dimensional quantum gravity,” Nucl. Phys. B 640
2002
Cited alongside, same era.
C. Meusburger and B. J. Schroers, “Poisson structure and symmetry in the Chern-Simons formulation of (2+1)-dimensional gravity,” Class. Quant. Grav. 20
2003
Cited alongside, same era.
2008
Later among the works it cites.
V. N. Tolstoy, “Twisted quantum deformations of Lorentz and Poincare algebras,” Bulg. J. Phys. 35
2008
Later among the works it cites.
K. Noui, “Three Dimensional Loop Quantum Gravity: Particles and the Quantum Double,” J. Math. Phys. 47 · 2009
Later among the works it cites.
2010
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
A. Ashtekar and J. Lewandowski, “Background independent quantum gravity: A status report,” Class. Quant. Grav. 21
T. Thiemann, “Modern Canonical Quantum General Relativity” Cambridge, UK: Cambridge Univ. Pr. (2007) 819 p; [arXiv:gr-qc/0110034] · 2004
Cited alongside, same era.
G. Amelino-Camelia, L. Smolin and A. Starodubtsev, “Quantum symmetry, the cosmological constant and Planck scale phenomenology,” Class. Quant. Grav. 21
2004
Cited alongside, same era.
L. Freidel, J. Kowalski-Glikman and L. Smolin, “2+1 gravity and doubly special relativity,” Phys. Rev. D 69
2004
Cited alongside, same era.
K. Noui and A. Perez, “Three-dimensional loop quantum gravity: Physical scalar product and spin foam models,” Class. Quant. Grav. 22
2005
Cited alongside, same era.
K. Noui and A. Perez, “Three-dimensional loop quantum gravity: Coupling to point particles,” Class. Quant. Grav. 22
2005
Cited alongside, same era.
C. Meusburger and B. J. Schroers, “Phase space structure of Chern-Simons theory with a non-standard puncture,” Nucl. Phys. B 738
2006
Cited alongside, same era.
L. Freidel and E. R. Livine, “Ponzano-Regge model revisited III: Feynman diagrams and effective field theory,” Class. Quant. Grav. 23
L. Freidel and E. R. Livine, “Effective 3-D quantum gravity and non-commutative quantum field theory,” Phys. Rev. Lett. 96 · 2006
Cited alongside, same era.
2011
Later among the works it cites.
K. Noui, A. Perez and D. Pranzetti, “Canonical quantization of non-commutative holonomies in 2+1 loop quantum gravity,” JHEP 1110 · 2012
Later among the works it cites.
G. Amelino-Camelia, “Quantum-space-time Phenomenology,” Living Rev. Rel. 16
2013
Later among the works it cites.
M. Bojowald and G. M. Paily, “Deformed General Relativity,” Phys. Rev. D 87
2013
Later among the works it cites.
D. Pranzetti, “Turaev-Viro amplitudes from 2+1 Loop Quantum Gravity,” Phys. Rev. D 89
2014
Later among the works it cites.
V. Bonzom, M. Dupuis and F. Girelli, “Towards the Turaev-Viro amplitudes from a Hamiltonian constraint,” Phys. Rev. D 90 · 2014
Later among the works it cites.
2016
Closest in time.
H. M. Haggard, M. Han, W. Kaminski and A. Riello, “SL(2,C) Chern-Simons Theory, a non-Planar Graph Operator, and 4D Loop Quantum Gravity with a Cosmological Constant: Semiclassical Geometry,” Nucl. Phys. B 900 · 2016
Closest in time.