Noncommutative fields and the short-scale structure of spacetime

There is a growing evidence that due to quantum gravity effects the effective spacetime dimensionality might change in the UV. In this letter we investigate this hypothesis by using quantum fields to derive the UV behaviour of the static, two point sources potential. We mimic quantum gravity effects by using non-commutative fields associated to a Lie group momentum space with a Planck mass curvature scale. We find that the static potential becomes finite in the short-distance limit. This indicates that quantum gravity effects lead to a dimensional reduction in the UV or, alternatively, that point-like sources are effectively smoothed out by the Planck scale features of the non-commutative quantum fields.Comment: 12 pages, 2 figure

Quantum Potential Approach to Quantum Cosmology

In this paper we discuss the quantum potential approach of Bohm in the context of quantum cosmological model. This approach makes it possible to convert the wavefunction of the universe to a set of equations describing the time evolution of the universe. Following Ashtekar et.\ al., we make use of quantum canonical transformation to cast a class of quantum cosmological models to a simple form in which they can be solved explicitly, and then we use the solutions to recover the time evolution.Comment: 17 pages,LaTeX. A newer version of this paper appears as gr-qc/9509040 since the author didn't use the replace command

Effective particle kinematics from Quantum Gravity

Particles propagating in de Sitter spacetime can be described by the topological BF \SO(4,1) theory coupled to point charges. Gravitational interaction between them can be introduced by adding to the action a symmetry breaking term, which reduces the local gauge symmetry down to \SO(3,1), and which can be treated as a perturbation. In this paper we focus solely on topological interactions which corresponds to zeroth order in this perturbative expansion. We show that in this approximation the system is effectively described by the \SO(4,1) Chern-Simons theory coupled to particles and living on the 3 dimensional boundary of space-time. Then, using Alekseev--Malkin construction we find the effective theory of particles kinematics. We show that the particles action contains standard kinetic terms and the deformation shows up in the presence of interaction terms. The strength of the interactions is proportional to deformation parameter, identified with Planck mass scale.Comment: 19 pages, 2 figure

Deformed discrete symmetries

We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of kappa-deformations of the Poincare algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter kappa to be derived via precision measurements of discrete symmetries and CPT.Comment: 10 pages, final version, to appear in PL