We propose a deepening of the relativity principle according to which the invariant arena for nonquantum physics is a phase space rather than spacetime. Descriptions of particles propagating and interacting in spacetimes are constructed by observers, but different observers, separated from each other by translations, construct different spacetime projections from the invariant phase space. Nonetheless, all observers agree that interactions are local in the spacetime coordinates constructed by observers local to them. This framework, in which absolute locality is replaced by relative locality, results from deforming energy-momentum space, just as the passage from absolute to relative simultaneity results from deforming the linear addition of velocities. Different aspects of energy-momentum space geometry, such as its curvature, torsion and nonmetricity, are reflected in different kinds of deformations of the energy-momentum conservation laws. These are in principle all measurable by appropriate experiments. We also discuss a natural set of physical hypotheses which singles out the cases of energy-momentum space with a metric compatible connection and constant curvature

Doubly Special Relativity (DSR) theory is a theory with two observerindependent 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 paper 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.

Doubly Special Relativity (DSR) theory is a recently proposed theory with two observerindependent scales (of velocity and mass), which is to describe a kinematic structure underlining the theory of Quantum Gravity. We observe that there are infinitely many DSR constructions of the energy-momentum sector, each of whose can be promoted to the κ-Poincaré quantum (Hopf) algebra. Then we use the co-product of this algebra and the Heisenberg double construction of κ-deformed phase space in order to derive the non-commutative space-time structure and the description of the whole of DSR phase space. Next we show that contrary to the ambiguous structure of the energy momentum sector, the space-time of the DSR theory is unique and related to the theory with non-commutative space-time proposed long ago by Snyder. This theory provides noncommutative version of Minkowski space-time enjoying ordinary Lorentz symmetry. It turns out that when one builds a natural phase space on this space-time, its intrinsic length parameter becomes observer-independent.

It has been observed recently by Giovanni Amelino-Camelia [3,4] 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

No abstract

We review the basic steps in building the asymptotic analysis of the Euclidean sector of new spin foam models using coherent states, for Immirzi parameter less than one. We focus on conceptual issues and by so doing omit peripheral proofs and the original discussion on spin structures.

We derive finite boost transformations based on the Lorentz sector of the bicross-product-basis kappa -Poincare 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. (C) 2001 Published by Elsevier Science B.V

Investigations of the possibility that some novel "quantum" properties of spacetime might induce a Planck-scale modification of the energy/momentum dispersion relation focused at first on scenarios with Planck-scale violations of Lorentz symmetry, with an associated reduced n-parameter (n < 6) rotation-boost symmetry group. More recently several studies have considered the possibility of a "doubly special relativity", in which the modification of the dispersion relation emerges from a framework with both the Planck scale and the speed-of-light scale as characteristic scales of a 6-parameter group of rotation-boost symmetry transformations (a deformation of the Lorentz transformations). For the schemes with broken Lorentz symmetry at the Planck scale there is a large literature on the derivation of experimental limits. We provide here a corresponding analysis for the doubly-special-relativity framework. We find that the analyses of photon stability, synchrotron radiation, and threshold conditions for particle production in collision processes, the three contexts which are considered as most promising for constraining the broken-Lorentz-symmetry scenario, cannot provide significant constraints on doubly-special-relativity parameter space. However, certain types of analyses of gamma-ray bursts are sensitive to the symmetry deformation. A key element of our study is an observation that removes a possible sign ambiguity for the doubly-special-relativity framework. This result also allows us to characterize more sharply the differences between the doubly-special-relativity framework and the framework of κ-Poincaré Hopf algebras, two frameworks which are often confused with each other in the literature. a While sometimes, especially when commenting on the logical structure of the DSR framework, it is convenient for us to indicate explicitly the speed-of-light scale c, in most equations we adopt conventions such that c = = 1.