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Based on deformed translations in the κ-anti-de Sitter algebra, we derive a delay in the time of detection between a soft and a hard photon, which are simultaneously emitted at a distant event, to first order in the quantum gravity parameter. In the basis analyzed, the trajectories are undeformed, and the effect depends exclusively on the symmetry properties of the quantum algebra. The time delay depends linearly on the energy of the hard particle and has a sinusoidal dependence on the redshift of the source.

We demonstrate a compatibility between the relativity principle and the clock postulate in deformed special relativity, by identifying the relevant deformed Lorentz transformations in position space between arbitrary frames. This result leads to a first-principles correction to the dilated lifetime of fundamental particles. It turns out that these modified time dilations offer a way to scrutinize Lorentz invariance (or deviations thereof) to high precision.

We show in general that for a relativistic theory with curved momentum space, i.e. a theory with deformed relativistic symmetries, the physical velocity of particles coincides with their group velocity. This clarifies a long-standing question about the discrepancy between coordinate and group velocity for this kind of theories. The first evidence that this was the case had been obtained at linear order in the deformation parameter in Ref. 1 for the specific case of κ -momentum space. The proof was based on the recent understanding of how relative locality affects these scenarios. Here we rely again on a careful implementation of relative locality effects, and obtain our result for a generic (relativistic) curved momentum space framework at all orders in the deformation/curvature parameter. We also discuss the validity of this result when the deformation depends on the coordinates as well as on the momenta. [ABSTRACT FROM AUTHOR]

Abstract: We consider a particular effect which can be expected in scenarios of deviations from special relativity induced by Planckian physics: the loss of additivity in the total energy of a system of particles. We argue about the necessity to introduce a length scale to control the effects of non-additivity for macroscopic objects and consider white dwarfs as an appropriate laboratory to test this kind of new physics. We study the sensitivity of the mass-radius relation of the Chandrasekhar model to these corrections by comparing the output of a simple phenomenological model to observational data of white dwarfs. [Copyright &y& Elsevier]

In this paper, an experimental verification of the relationship between the deformed Minkowsky space-time and the piezonuclear emission has been obtained by testing several cylindrical steel bars cyclically loaded in a mechanical fatigue machine. During the compression cycles, α-particles have been both detected by a () scintillator and a Geiger counter. Taking into account the theory of the deformed special relativity, we report that the emission only occurs after a specific value of energy is overcome. This value is strictly related to the weak and strong nuclear interactions, which in turn define the regions of Minkowsky and non-Minkowsky space-time. [ABSTRACT FROM AUTHOR]

We show that, in the framework of Deformed Special Relativity (DSR), namely a (four-dimensional) generalization of the (local) space-time structure based on an energy-dependent "deformation" of the usual Minkowski geometry, two kinds of gauge symmetries arise, whose spaces either coincide with the deformed Minkowski space or are just internal spaces to it. This is why we named them "metric gauge theories". In the case of the internal gauge fields, they are a consequence of the deformed Minkowski space (DMS) possessing the structure of a generalized Lagrange space. Such a geometrical structure allows one to define curvature and torsion in the DMS. [ABSTRACT FROM AUTHOR]

The wave equation for spinless particles with the Lorentz violating term is considered. We formulate the third-order in derivatives wave equation leading to the modified dispersion relation. The first-order formalism is considered and the density matrix is obtained. The Schrödinger form of equations is presented and the quantum-mechanical Hamiltonian is found. Exact solutions of the wave equation are obtained for particles in the constant and uniform external magnetic field. The change of the synchrotron radiation radius due to quantum gravity corrections is calculated. [ABSTRACT FROM AUTHOR]

We explore some novel consequences of Born's reciprocal relativity theory in flat phase-space and generalize the theory to the curved space-time scenario. We provide, in particular, six specific results resulting from Born's reciprocal relativity and which are not present in special relativity. These are: momentum-dependent time delay in the emission and detection of photons; energy-dependent notion of locality; superluminal behavior; relative rotation of photon trajectories due to the aberration of light; invariance of areas-cells in phase-space and modified dispersion relations. We finalize by constructing a Born reciprocal general relativity theory in curved space-time which requires the introduction of a complex Hermitian metric, torsion and nonmetricity. The latter procedure can be extended to the curved phase-space scenario. [ABSTRACT FROM AUTHOR]

A framework is proposed for field theory with a new energy scale. The proposal is based on the idea, appearing for example in Deformed Special Relativity (DSR), of building phenomenological models for quantum gravity by taking momentum space to be curved rather than flat. In this work, this idea is implemented by introducing a fifth dimension and by imposing an extra constraint on physical field configurations in addition to the mass shell constraint. Advantages of this approach are that Lorentz symmetry is explicitly preserved and that an interacting scalar field model constructed in this way can be shown to be unitary. Implications for electrodynamics are discussed but the interpretation of the extra dimension needs to be clarified before making predictions for experiments. [ABSTRACT FROM AUTHOR]

Abstract: We investigate how deformations of special relativity in momentum space can be extended to position space in a consistent way, such that the dimensionless contraction between wave-vector and coordinate-vector remains invariant. By using a parametrization in terms of an energy dependent speed of light, and an energy dependent Planck''s constant, we are able to formulate simple requirements that completely determine the active transformations in position space. These deviate from the standard transformations for large velocities of the observed object. Some examples are discussed, and it is shown how the relativistic mass gain of a massive particle is affected. We finally study the construction of passive Lorentz-transformations. [Copyright &y& Elsevier]

We apply Lie algebra deformation theory to the problem of identifying the stable form of the quantum relativistic kinematical algebra. As a warm up, given Galileo's conception of spacetime as input, some modest computer code we wrote zeroes in on the Poincaré-plus-Heisenberg algebra in about a minute. Further ahead, along the same path, lies a three-dimensional deformation space, with an instability double cone through its origin. We give physical as well as geometrical arguments supporting our view that moment, rather than position operators, should enter as generators in the Lie algebra. With this identification, the deformation parameters give rise to invariant length and mass scales. Moreover, standard quantum relativistic kinematics of massive, spinless particles corresponds to non-commuting moment operators, a purely quantum effect that bears no relation to spacetime non-commutativity, in sharp contrast to earlier interpretations. [ABSTRACT FROM AUTHOR]

A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a model including single- or multi-interaction processes, for which absolute locality in terms of canonical spacetime coordinates is lost. We discuss the different alternatives for observable effects in the propagation of a particle over very large distances that emerge from the new notion of spacetime. A central ingredient in the discussion is the cluster decomposition principle, which can be used to favor some alternatives over the others. [ABSTRACT FROM AUTHOR]