Noisy soccer balls

In her Comment arXiv:1202.4066 [hep-th] Hossenfelder proposes a generalization of the results we reported in Phys. Rev. D84 (2011) 087702 and argues that thermal fluctuations introduce incurable pathologies for the description of macroscopic bodies in the relative-locality framework. We here show that Hossenfelders analysis, while raising a very interesting point, is incomplete and leads to incorrect conclusions. Her estimate for the fluctuations did not take into account some contributions from the geometry of momentum space which must be included at the relevant order of approximation. Using the full expression here derived one finds that thermal fluctuations are not in general large for macroscopic bodies in the relative-locality framework. We find that such corrections can be unexpectedly large only for some choices of momentum-space geometry, and we comment on the possibility of developing a phenomenology suitable for possibly ruling out such geometries of momentum space.

Wheeler-De Witt equation and AdS/CFT correspondence

The radial Wheeler--De Witt equation on the asymptotically AdS spacetime proposed in [9] has as its semiclassical solution the wave function that asymptotically satisfies the conformal Ward identity, exemplifying the AdS/CFT correspondence. In this paper we show that this results holds also in the case of a complete quantum solution of the radial Wheeler--De Witt equation. It turns out that if the wavefunction is expanded in the parameter $rho$ with $rhorightarrow0$ defines the asymptotic boundary of the spacetime, the quantum loop corrections to the semiclassical wave are of subleading order.

Curved Momentum Space and Relative Locality

I briefly discuss the construction of a theory of particles with curved momentum space and its consequence, the principle of relative locality.

$kappa$-Minkowski space, scalar field, and the issue of Lorentz invariance

We describe $kappa$-Minkowski space and its relation to group theory. The group theoretical picture makes it possible to analyze the symmetries of this space. As an application of this analysis we analyze in detail free field theory on $kappa$-Minkowski space and the Noether charges associated with deformed spacetime symmetries.