Relative Locality, Kappa-Poincaré and the Relativity Principle

          @misc{ pirsa_PIRSA:11110138,
            doi = {10.48660/11110138},
            url = {https://pirsa.org/11110138},
            author = {Mercati, Flavio},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Relative Locality, Kappa-Poincar{\'e} and the Relativity Principle},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {nov},
            note = {PIRSA:11110138 see, \url{https://pirsa.org}}
          }
          

Abstract

I briefly introduce the recently introduced idea of relativity of locality, which is a consequence of a non-flat geometry of momentum space. Momentum space can acquire nontrivial geometrical properties due to quantum gravity effects. I study the relation of this framework with noncommutative geometry, and the Quantum Group approach to noncommutative spaces. In particular I'm interested in kappa-Poincaré, which is a Quantum Group that, as shown by Freidel and Livine, in the 1+1D case emerges as the symmetry of effective field theory coupled with quantum gravity, once that the gravitational degrees of freedom are integrated out. I'm interested in particular in the Lorentz covariance of this model which is present, but is realized in a nontrivial way. If I still have time, I'll then speak about an under-course general study of the Lorentz covariance of Relative Locality models.