$\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems

Abstract

Some classes of Deformed Special Relativity (DSR) theories are reconsidered within the Hopf algebraic formulation. For this purpose we shall explore a minimal framework of deformed Weyl-Heisenberg algebras provided by a smash product construction of DSR algebra. It is proved that this DSR algebra, which uniquely unifies $\kappa$-Minkowski spacetime coordinates with Poincaré generators, can be obtained by nonlinear change of generators from undeformed one. Its various realizations in terms of the standard (undeformed) Weyl-Heisenberg algebra opens the way for quantum mechanical interpretation of DSR theories in terms of relativistic (Stückelberg version) Quantum Mechanics. On this basis we review some recent results concerning twist realization of $\kappa$-Minkowski spacetime described as a quantum covariant algebra determining a deformation quantization of the corresponding linear Poisson structure. Formal and conceptual issues concerning quantum $\kappa$-Poincaré and $\kappa$-Minkowski algebras as well as DSR theories are discussed. Particularly, the so-called "$q$-analog" version of DSR algebra is introduced. Is deformed special relativity quantization of doubly special relativity remains an open question. Finally, possible physical applications of DSR algebra to description of some aspects of Planck scale physics are shortly recalled.

References in corpus (35)

• Electrodynamics with Lorentz-violating operators of arbitrary dimension
• A Gravity Theory on Noncommutative Spaces
• Probing quantum gravity using photons from a flare of the active galactic nucleus Markarian 501 observed by the MAGIC telescope
• Symmetry, Gravity and Noncommutativity
• Prospects for constraining quantum gravity dispersion with near term observations
• Kappa-Minkowski space-time and the star product realizations
• New realizations of Lie algebra kappa-deformed Euclidean space
• Twisted Statistics in kappa-Minkowski Spacetime
• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• Covariant realizations of kappa-deformed space
• Twisted Gauge Theories
• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Gauge theories on the kappa-Minkowski spacetime
• From noncommutative kappa-Minkowski to Minkowski space-time
• Bounds on an energy-dependent and observer-independent speed of light from violations of locality
• A Lagrangian for DSR Particle and the Role of Noncommutativity
• A no-pure-boost uncertainty principle from spacetime noncommutativity
• kappa-deformed Spacetime From Twist
• Covariant Realization of Quantum Spaces as Star Products by Drinfeld Twists
• On kappa-deformation and triangular quasibialgebra structure
• Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology
• Twisted Quantum Deformations of Lorentz and Poincaré algebras
• Emergent non-commutative matter fields from Group Field Theory models of quantum spacetime
• Noncommutative Geometry of Super-Jordanian $OS{p}_h(2/1)$ Covariant Quantum Space
• Jordanian Twist Quantization of D=4 Lorentz and Poincare Algebras and D=3 Contraction Limit
• The Stabilized Poincare-Heisenberg algebra: a Clifford algebra viewpoint
• Chains of extended Jordanian twists for Lie superalgebras
• Comments on Nonlocality in Deformed Special Relativity, in reply to arXiv:1004.0664 by Lee Smolin and arXiv:1004.0575 by Jacob et al
• Quantum $\kappa$-Poincaré Algebra from de Sitter Space of Momenta
• Reply to arXiv:1006.2126 by Giovanni Amelino-Camelia et al
• Canonical k-Minkowski Spacetime
• DSR and Canonical Transformations: A Comment on a ``A Lagrangian for DSR particle and the role of noncommutativity''
• New twisted quantum deformations of D=4 super-Poincare algebra
• Realization of q-deformed spacetime as star product by a Drinfeld twist

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