kappa-Minkowski spacetime as the result of Jordanian twist deformation

Abstract

Two one-parameter families of twists providing kappa-Minkowski * -product deformed spacetime are considered: Abelian and Jordanian. We compare the derivation of quantum Minkowski space from two perspectives. The first one is the Hopf module algebra point of view, which is strictly related with Drinfeld's twisting tensor technique. The other one relies on an appropriate extension of "deformed realizations" of nondeformed Lorentz algebra by the quantum Minkowski algebra. This extension turns out to be de Sitter Lie algebra. We show the way both approaches are related. The second path allows us to calculate deformed dispersion relations for toy models ensuing from different twist parameters. In the Abelian case one recovers kappa-Poincar'e dispersion relations having numerous applications in doubly special relativity. Jordanian twists provide a new type of dispersion relations which in the minimal case (related to Weyl-Poincar'e algebra) takes an energy-dependent linear mass deformation form.

23 pages, Revtex4, one comment added, version to be published in Phys. Rev. D

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• The $\kappa$-(A)dS noncommutative spacetime
• Three-dimensional gravity and Drinfel'd doubles: spacetimes and symmetries from quantum deformations
• The kappa-(A)dS quantum algebra in (3+1) dimensions
• Gauge theories on quantum spaces
• Differential Structure on kappa-Minkowski Spacetime Realized as Module of Twisted Weyl Algebra
• Braided $L_{\infty }$-Algebras, Braided Field Theory and Noncommutative Gravity
• The 2D $\kappa$-Dirac oscillator
• $k$-Minkowski-deformation of $U(1)$ gauge theory
• $\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Field Theory on Curved Noncommutative Spacetimes
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Dispersion Relations in $\kappa$-Noncommutative Cosmology
• Cayley-Klein Lie bialgebras: Noncommutative spaces, Drinfel'd doubles and kinematical applications
• Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics
• Coisotropic Lie bialgebras and complementary dual Poisson homogeneous spaces
• All noncommutative spaces of $\kappa$-Poincaré geodesics
• Generalized quantum phase spaces for the $\kappa$-deformed extended Snyder model
• The noncommutative space of light-like worldlines
• Families of vector-like deformed relativistic quantum phase spaces, twists and symmetries
• $\kappa$-General-Relativity I: a Non-Commutative GR Theory with the $\kappa$-Minkowski Spacetime as its Flat Limit
• On interpolations between Jordanian twists
• Interpolations between Jordanian twists, the Poincaré-Weyl algebra and dispersion relations
• Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups