Classical basis for kappa-Poincare algebra and doubly special relativity theories

Abstract

Several issues concerning quantum kappa-Poincare algebra are discussed and reconsidered here. We propose two different formulations of kappa-Poincare quantum algebra. Firstly we present a complete Hopf algebra formulae of kappa-Poincare in classical Poincare basis. Further by adding one extra generator, which modifies the classical structure of Poincare algebra, we eliminate non polynomial functions in the kappa-parameter. Hilbert space representations of such algebras make Doubly Special Relativity (DSR) similar to the Stueckelberg's version of (proper-time) relativistic Quantum Mechanics.

14 pages in Revtex4, final published version (revised and extended)

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• Phenomenological consequences of a geometry in the cotangent bundle
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• Deformed Covariant Quantum Phase Spaces as Hopf Algebroids
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• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• Beyond Special Relativity at second order
• Twisting and kappa-Poincare
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• $\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Constraints on the deformation scale of a geometry in the cotangent bundle
• A bound on Planck-scale deformations of CPT from muon lifetime
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• Geometry of multi-particle systems with a relativistic deformed kinematics and the relative locality principle
• Maximally extended sl(2|2), q-deformed d(2,1;epsilon) and 3D kappa-Poincaré
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Light-like $\kappa$-deformations and scalar field theory via Drinfeld twist
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• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• A group theoretic description of the $\kappa$-Poincaré Hopf algebra
• A short introduction to $\kappa$-deformation
• Modification of the mean free path of very high energy photons due to a relativistic deformed kinematics
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• Twin Peaks: A possible signal in the production of resonances beyond special relativity
• Generalized quantum phase spaces for the $\kappa$-deformed extended Snyder model
• A new perspective on Doubly Special Relativity
• Space-time thermodynamics in momentum dependent geometries
• Mixing coproducts for theories with particle-dependent relativistic properties
• Equilibrium properties of blackbody radiation with an ultraviolet energy cut-off
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• $\kappa$-General-Relativity I: a Non-Commutative GR Theory with the $\kappa$-Minkowski Spacetime as its Flat Limit
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• Bicrossproduct construction versus Weyl-Heisenberg algebra
• Exploring black hole mechanics in cotangent bundle geometries
• Twist deformations leading to kappa-Poincare Hopf algebra and their application to physics
• Coherence and Entanglement in a Non-commutative Spacetime
• Star-products for Lie-algebraic noncommutative Minkowski space-times
• Photon Absorption in a Doubly Special Relativity Model with Undeformed Free Propagation and Total Momentum Conservation
• Realizations of the Extended Snyder Model