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4.0
Jun 28, 2018
06/18
by
Leonardo Barcaroli; Giulia Gubitosi
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We present the first detailed study of the kinematics of free relativistic particles whose symmetries are described by a quantum deformation of the de Sitter algebra, known as $q$-de Sitter Hopf algebra. The quantum deformation parameter is a function of the Planck length $\ell$ and the de Sitter radius $H^{-1}$, such that when the Planck length vanishes, the algebra reduces to the de Sitter algebra, while when the de Sitter radius is sent to infinity one recovers the $\kappa$-Poincar\'e Hopf...
Topic: General Relativity and Quantum Cosmology
Source: http://arxiv.org/abs/1512.03462
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12
Jun 26, 2018
06/18
by
Niccoló Loret; Leonardo Barcaroli
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This proceeding is based on a talk prepared for the XIII Marcell Grossmann meeting. We summarise some results of work in progress in collaboration with Giovanni Amelino-Camelia about momentum dependent (Rainbow) metrics in a Relative Locality framework and we show that this formalism is equivalent to the Hamiltonian formalization of Relative Locality obtained in arXiv:1102.4637.
Topics: High Energy Physics - Theory, General Relativity and Quantum Cosmology
Source: http://arxiv.org/abs/1501.03698
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54
Sep 20, 2013
09/13
by
Niccoló Loret; Leonardo Barcaroli; Giacomo Rosati
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We summarize some of the results we obtained in arXiv:1006.2126 (Physical Review Letters 106, 071301), arXiv:1102.4637 (Physics Letters B 700, 150-156) and in arXiv:1107.3334, giving complementary characterizations of the relativity of spacetime locality that affects certain Planck-scale-deformed phase-space descriptions of free particles.
Source: http://arxiv.org/abs/1207.4441v1
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86
Jul 20, 2013
07/13
by
Giovanni Amelino-Camelia; Leonardo Barcaroli; Niccoló Loret
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We investigate some aspects of relativistic classical theories with "relative locality", in which pairs of events established to be coincident by nearby observers may be described as non-coincident by distant observers. While previous studies focused mainly on the case of longitudinal relative locality, where the effect occurs along the direction connecting the distant observer to the events, we here focus on transverse relative locality, in which instead the effect is found in a...
Source: http://arxiv.org/abs/1107.3334v1
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16
Jun 28, 2018
06/18
by
Leonardo Barcaroli; Lukas K. Brunkhorst; Giulia Gubitosi; Niccoló Loret; Christian Pfeifer
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We describe the Hamilton geometry of the phase space of particles whose motion is characterised by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a simultaneous description of both spacetime curvature and non-trivial momentum space geometry. We consider as explicit examples two models for Planck-scale modified dispersion relations, inspired from the $q$-de Sitter and $\kappa$-Poincar\'e quantum groups. In the first...
Topics: General Relativity and Quantum Cosmology, High Energy Physics - Theory
Source: http://arxiv.org/abs/1507.00922
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3.0
Jun 29, 2018
06/18
by
Leonardo Barcaroli; Lukas K. Brunkhorst; Giulia Gubitosi; Niccoló Loret; Christian Pfeifer
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The covariant understanding of dispersion relations as level sets of Hamilton functions on phase space enables us to derive the most general dispersion relation compatible with homogeneous and isotropic spacetimes. We use this concept to present a Planck-scale deformation of the Hamiltonian of a particle in Friedman-Lema\^itre-Robertson-Walker (FLRW) geometry that is locally identical to the $\kappa$-Poincar\'e dispersion relation, in the same way as the dispersion relation of point particles...
Topics: High Energy Physics - Theory, General Relativity and Quantum Cosmology
Source: http://arxiv.org/abs/1612.01390
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6.0
Jun 30, 2018
06/18
by
Giovanni Amelino-Camelia; Leonardo Barcaroli; Giulia Gubitosi; Stefano Liberati; Niccoló Loret
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Finsler geometry is a well known generalization of Riemannian geometry which allows to account for a possibly non trivial structure of the space of configurations of relativistic particles. We here establish a link between Finsler geometry and the sort of models with curved momentum space and DSR-relativistic symmetries which have been recently of interest in the quantum-gravity literature. We use as case study the much-studied scenario which is inspired by the $\kappa$-Poincar\'e quantum...
Topics: High Energy Physics - Theory, General Relativity and Quantum Cosmology
Source: http://arxiv.org/abs/1407.8143
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4.0
Jun 30, 2018
06/18
by
Leonardo Barcaroli; Lukas K. Brunkhorst; Giulia Gubitosi; Niccoló Loret; Christian Pfeifer
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We use our previously developed identification of dispersion relations with Hamilton functions on phase space to locally implement the $\kappa$-Poincar\'e dispersion relation in the momentum spaces at each point of a generic curved spacetime. We use this general construction to build the most general Hamiltonian compatible with spherical symmetry and the Plank-scale-deformed one such that in the local frame it reproduces the $\kappa$-Poincar\'e dispersion relation. Specializing to...
Topics: General Relativity and Quantum Cosmology, High Energy Physics - Theory
Source: http://arxiv.org/abs/1703.02058