Doubly Special Relativity (DSR) theory is a theory with two observer-independent scales, of velocity and mass (or length). Such a theory has been proposed by Amelino-Camelia as a kinematic structure ...which may underline quantum theory of relativity. Recently another theory of this kind has been proposed by Magueijo and Smolin. In this Letter we show that both these theories can be understood as particular bases of the
κ-Poincaré theory based on quantum (Hopf) algebra. This observation makes it possible to construct the space–time sector of Magueijo and Smolin DSR. We also show how this construction can be extended to the whole class of DSRs. It turns out that for all such theories the structure of space–time commutators is the same. This results lead us to the claim that physical predictions of properly defined DSR theory should be independent of the choice of basis.
It has been observed recently by Amelino-Camelia that the hypothesis of existence of a minimal observer-independent (Planck) length scale is hard to reconcile with special relativity. As a remedy he ...postulated to modify special relativity by introducing an observer-independent length scale. In this Letter we set forward a proposal how one should modify the principles of special relativity, so as to assure that the value of mass scale is the same for any inertial observer. It turns out that one can achieve this by taking dispersion relations such that the speed of light goes to infinity for finite momentum (but infinite energy), proposed in the framework of the quantum
κ-Poincaré symmetry. It follows that at the Planck scale the world may be non-relativistic.
We revisit the “brick wall” model for black hole entropy taking into account backreaction effects on the horizon structure. We do so by adopting an evaporating metric in the quasi-static ...approximation in which departures from the standard Schwarzschild metric are governed by a small luminosity factor. One of the effects of the backreaction is to create an ergosphere-like region which naturally tames the usual divergence in the calculation of the partition function of the field. The black hole luminosity sets the width of such ‘quantum ergosphere’. We find a finite horizon contribution to the entropy which, for the luminosity associated to the Hawking flux, reproduces remarkably well the Bekenstein-Hawking entropy-area law.
We derive finite boost transformations based on the Lorentz sector of the bicross-product-basis κ-Poincaré Hopf algebra. We emphasize the role of these boost transformations in a recently-proposed ...new relativistic theory, and their relevance for experimental studies presently being planned. We find that when the (dimensionful) deformation parameter is identified with the Planck length, which together with the speed-of-light constant has the status of observer-independent scale in the new relativistic theory, the deformed boosts saturate at the value of momentum that corresponds to the inverse of the Planck length.
This paper explores the possibility of using Maxwell algebra and its generalizations called resonant algebras for the unified description of topological insulators. We offer the natural action ...construction, which includes the relativistic Wen-Zee and other terms, with adjustable coupling constants. By gauging all available resonant algebras formed by Lorentz, translational and Maxwell generators {Ja,Pa,Za} we present six Chern-Simons Lagrangians with various terms content accounting for different aspects of the topological insulators.
Additionally, we provide complementary actions for another invariant metric form, which might turn out useful in some generalized (2+1) gravity models.
Following the procedure proposed recently by Martin and Brandenberger we investigate the spectrum of the cosmological perturbations in the case when the “trans-Plackian” dispersion relations are ...motivated by the quantum
κ-Poincaré algebra. We find that depending on the choice of initial conditions of the perturbations, the spectrum either differs from the flat one for instantaneous Minkowski vacuum or, in the case of initial conditions minimizing energy density, leads to the observed scale-invariant Harrison–Zel'dovich spectrum in the Friedmann epoch.
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