Gianluca Mandanici

Group velocity in noncommutative spacetime

The realization that forthcoming experimental studies, such as the ones planned for the GLAST space telescope, will be sensitive to Planck-scale deviations from Lorentz symmetry has increased interest in noncommutative spacetimes, in which this type of effect is expected. We focus here on κ-Minkowski spacetime, a much-studied example of Lie-algebra noncommutative spacetime, but our analysis appears to be applicable to a more general class of noncommutative spacetimes. A technical controversy which has significant implications for experimental testability is the one concerning the κ-Minkowski relation between group velocity and momentum. A large majority of studies adopted the familiar relation v = dE(p)/dp, where E(p) is the κ-Minkowski dispersion relation, but recently some authors advocated alternative formulae. While in these previous studies the relation between group velocity and momentum was introduced through ad hoc formulae, we rely on a direct analysis of wave propagation in κ-Minkowski. Our results lead conclusively to the relation v = dE(p)/dp. We also show that the previous proposals of alternative velocity/momentum relations implicitly relied on an inconsistent implementation of functional calculus on κ-Minkowski and/or on an inconsistent description of spacetime translations.

GRAVITY IN QUANTUM SPACE–TIME

The literature on quantum-gravity-inspired scenarios for the quantization of space–time has so far focused on particle-physics-like studies. This is partly justified by the present limitations of our understanding of quantum gravity theories, but we here argue that valuable insight can be gained through semi-heuristic analyses of the implications for gravitational phenomena of some results obtained in the quantum space–time literature. In particular, we show that the types of description of particle propagation that emerged in certain quantum space–time frameworks have striking implications for gravitational collapse and for the behavior of gravity at large distances.

CORNWALL JACKIW TOMBOULIS EFFECTIVE POTENTIAL FOR CANONICAL NONCOMMUTATIVE FIELD THEORIES

We apply the Cornwall–Jackiw–Tomboulis (CJT) formalism to the scalar λφ4 theory in canonical-noncommutative space–time. We construct the CJT effective potential and the gap equation for general values of the noncommutative parameter θμν. We observe that under the hypothesis of translational invariance, which is assumed in the effective potential construction, differently from the commutative case (θμν=0), the renormalizability of the gap equation is incompatible with the renormalizability of the effective potential. We argue that our result, is consistent with previous studies, suggesting that a uniform ordered phase would be inconsistent with the infrared structure of canonical noncommutative theories.

Rainbow’s stars

In recent years, a growing interest in the equilibrium of compact astrophysical objects like white dwarf and neutron stars has been manifested. In particular, various modifications due to Planck-scale energy effects have been considered. In this paper we analyze the modification induced by gravity’s rainbow on the equilibrium configurations described by the Tolman–Oppenheimer–Volkoff (TOV) equation. Our purpose is to explore the possibility that the rainbow Planck-scale deformation of space-time could support the existence of different compact stars.

Gravity's Rainbow and Compact Stars

A number of recent studies has focused on the implications of new physics at the Planck scale on the equilibrium of compact astrophysical objects such as white dwarf and neutron stars. Here we analyze the modification of the equilibrium configurations induced by the so-called Gravitys Rainbow that account for Planck scale deformation of the space-time.

FINITE ZERO POINT GRAVITATIONAL ENERGY IN THE CONTEXT OF MODIFIED DISPERSION RELATIONS

We compute the Zero Point Energy in a spherically symmetric background distorted at high energy as predicted by Gravitys Rainbow. In this context we setup a Sturm-Liouville problem with the cosmological constant considered as the associated eigenvalue. The eigenvalue equation is a reformulation of the Wheeler-DeWitt equation. We find that the ordinary divergences can here be handled by an appropriate choice of the rainbows functions, in contrast to what happens in other conventional approaches.

On the invariance of the relative rest in doubly special relativity

In the framework of the most-studied doubly special relativity models the use of the naive formula v = dE/dp has been argued to lead to inconsistencies connected to different rules of transformation, under boosts, of particles with the same energy but with different masses. In this paper, we show that, at least in 1 + 1 dimensions, doubly special relativity can be formulated in such a way that the formula v = dE/dp is fully consistent with the invariance of the relative rest, easily fitting to the relativity principle. It is also argued that, always in 1 + 1 dimensions, is not necessary to renounce to the usual (commutative) Minkowski spacetime endowed with energy-independent boost transformations. The compatibility of the approach with superluminal propagation, with linear addition rule for energy, and possible extensions to 3 + 1 dimensions are also discussed.