Threedimensional gravity and deformations of relativistic symmetries
Abstract
It is possible that relativistic symmetries become deformed in the semiclassical regime of quantum gravity. Mathematically, such deformations lead to the noncommutativity of spacetime geometry and nonvanishing curvature of momentum space. The best studied example is given by the $\kappa$Poincaré Hopf algebra, associated with $\kappa$Minkowski space. On the other hand, the curved momentum space is a wellknown feature of particles coupled to threedimensional gravity. The purpose of this thesis was to explore some properties and mutual relations of the above two models. In particular, I study extensively the spectral dimension of $\kappa$Minkowski space. I also present an alternative limit of the ChernSimons theory describing threedimensional gravity with particles. Then I discuss the spaces of momenta corresponding to conical defects in higher dimensional spacetimes. Finally, I consider the Fock space construction for the quantum theory of particles in threedimensional gravity.
 Publication:

arXiv eprints
 Pub Date:
 November 2015
 arXiv:
 arXiv:1511.00674
 Bibcode:
 2015arXiv151100674T
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 78 pages, 6 figures. A thesis for the PhD degree in Physics