Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 125, 12 pages      arXiv:0712.4024      http://dx.doi.org/10.3842/SIGMA.2007.125
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

WKB Approximation in Noncommutative Gravity

Maja Buric a, John Madore b and George Zoupanos c
a) Faculty of Physics, University of Belgrade, P.O. Box 368 RS-11001 Belgrade, Serbia
b) Laboratoire de Physique Théorique, Université de Paris-Sud, Bâtiment 211, F-91405 Orsay, France
c) Physics Department, National Technical University, Zografou Campus, GR-15780 Athens

Received October 25, 2007, in final form December 21, 2007; Published online December 24, 2007

Abstract
We consider the quasi-commutative approximation to a noncommutative geometry defined as a generalization of the moving frame formalism. The relation which exists between noncommutativity and geometry is used to study the properties of the high-frequency waves on the flat background.

Key words: noncommutative geometry; models of quantum gravity.

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References

  1. Madore J., An introduction to noncommutative differential geometry and its physical applications, 2nd ed., London Mathematical Society Lecture Note Series, no. 257, Cambridge University Press, 2000.
  2. Buric M., Madore J., A dynamical 2-dimensional fuzzy space, Phys. Lett. B 622 (2005), 183-191, hep-th/0507064.
  3. Buric M., Grammatikopoulos T., Madore J., Zoupanos G., Gravity and the structure of noncommutative algebras, J. High Energy Phys. 2006 (2006), no. 04, 054, 17 pages, hep-th/0603044.
  4. Sahni V., Starobinsky A., Reconstructing dark energy, Internat. J. Modern Phys. D 15 (2006), 2105-2132, astro-ph/0610026.
  5. Cardella M.A., Zanon D., Noncommutative deformation of four dimensional Einstein gravity, Classical Quantum Gravity 20 (2003), L95-L104, hep-th/0212071.
  6. Garcia-Compean H., Obregon O., Ramirez C., Sabido M., Noncommutative self-dual gravity, Phys. Rev. D 68 (2003), 044015, 8 pages, hep-th/0302180.
  7. Aschieri P., Blohmann C., Dimitrijevic M., Meyer F., Schupp P., Wess J., A gravity theory on noncommutative spaces, Classical Quantum Gravity 22 (2005), 3511-3532, hep-th/0504183.
  8. Aschieri P., Dimitrijevic M., Meyer F., Wess J., Noncommutative geometry and gravity, Classical Quantum Gravity 23 (2006), 1883-1912, hep-th/0510059.

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