Noncommutative covariant spacetimes as a symmetry based approach to effective quantum gravity
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[1] Universidad de Burgos
Universidad de Burgos
Burgos, España
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- Localización: IV Jornadas de doctorandos de la Universidad de Burgos: Universidad de Burgos, 13 y 14 de diciembre de 2017 / coord. por José Luis Cuesta Gómez; Joaquín A. Pacheco Bonrostro (dir.), 2017, ISBN 978-84-16283-41-5, págs. 129-132
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
ln this short talk l will present some features of the effective approach to quantum gravity based on noncommutative geometry in the sense of quantum groups. Firstly, I will give some intuitive arguments on how the introduction of the main ideas of quantum mechanics in the description of spacetime should imply some modification of spacetime at Planckian scales.
Then, I will explain how a modification ofthe group of symmetries of general relativity induced by the presence of the Planck length as a second relativistic invariant gives rise to a noncommutativity among the coordinates on the spacetime manifold M. This noncommutativity, at the semiclassical level, is governed by a Poisson structure on M, and in the maximally symmetric cases considered the group of modified symmetries is a Poisson-Lie group. ln other words, the appropriate notion of invariance inherited from General Relativity is maintained.
Finally, l will comment on a different but related implication of the introduction of the Planck length, namely the nontrivial structure of momentum space. I will make emphasis on how the old intuition known as Bom reciprocity, stating a kind of duality between coordinates and momenta, finds a natural setting inside these noncommutative theories. In particular, l will present some recent results linking quantum deformations and curvature of both spacetime and momentum space.
