Two-dimensional gravity with an invariant energy scale and arbitrary dilaton potential

We investigate a model of two-dimensional gravity with arbitrary scalar potential obtained by gauging a deformation of de Sitter or more general algebras, which accounts for the existence of an invariant energy scale. We obtain explicit solutions of the field equations and discuss their properties.Comment: 8 pages, LaTe

Spherically symmetric solutions in four-dimensional Poincar\'e gravity with non-trivial torsion

We study a four-dimensional gauge theory of the Poincar\'e group with topological action which generalizes some well-known two-dimensional gravity models. We classify the spherically symmetric solutions and discuss the perturbative propagation of excitations around flat spacetime.Comment: 12 pages, plain Te

Classical dynamics on Snyder spacetime

We study the classical dynamics of a particle in Snyder spacetime, adopting the formalism of constrained Hamiltonian systems introduced by Dirac. We show that the motion of a particle in a scalar potential is deformed with respect to special relativity by terms of order \beta E^2. An important result is that in the relativistic Snyder model a consistent choice of the time variable must necessarily depend on the dynamics.Comment: 8 pages, LaTeX. The choice of gauge in the original version was inconsistent with the dynamics. This error has been correcte

Classical and quantum mechanics of the nonrelativistic Snyder model in curved space

The Snyder-de Sitter (SdS) model is a generalization of the Snyder model to a spacetime background of constant curvature. It is an example of noncommutative spacetime admitting two fundamental scales besides the speed of light, and is invariant under the action of the de Sitter group. Here we consider its nonrelativistic counterpart, i.e. the Snyder model restricted to a three-dimensional sphere, and the related model obtained by considering the anti-Snyder model on a pseudosphere, that we call anti-Snyder-de Sitter (aSdS). By means of a nonlinear transformation relating the SdS phase space variables to canonical ones, we are able to investigate the classical and the quantum mechanics of a free particle and of an oscillator in this framework. As in their flat space limit, the SdS and aSdS models exhibit rather different properties. In the SdS case, a lower bound on the localization in position and momentum space arises, which is not present in the aSdS model. In the aSdS case, instead, a specific combination of position and momentum coordinates cannot exceed a constant value. We explicitly solve the classical and the quantum equations for the motion of the free particle and of the harmonic oscillator. In both the SdS and aSdS cases, the frequency of the harmonic oscillator acquires a dependence on the energy.Comment: 21 pages; discussion of three-dimensional quantum mechanics added, error in quantum commutators correcte

Hamiltonian formalism and spacetime symmetries in generic DSR models

We study the structure of the phase space of generic models of deformed special relativity that gives rise to a definition of velocity consistent with the deformed Lorentz symmetry. As a byproduct we also determine the laws of transformation of spacetime coordinates.Comment: 10 pages TeX; v.2 completely rewritten; v.4 some typos corrected and some points clarifie