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

References in corpus (22)

• A Gravity Theory on Noncommutative Spaces
• Symmetry, Gravity and Noncommutativity
• Kappa-Minkowski space-time and the star product realizations
• New realizations of Lie algebra kappa-deformed Euclidean space
• Corrections to Schwarzschild Solution in Noncommutative Gauge Theory of Gravity
• 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
• Twisting all the way: from Classical Mechanics to Quantum Fields
• Gauge theories on the kappa-Minkowski spacetime
• From noncommutative kappa-Minkowski to Minkowski space-time
• Lie algebraic Noncommutative Gravity
• A Lagrangian for DSR Particle and the Role of Noncommutativity
• On Black Holes and Cosmological Constant in Noncommutative Gauge Theory of Gravity
• kappa-deformed Spacetime From Twist
• Star products made (somewhat) easier
• Noncommutative fields and actions of twisted Poincare algebra
• Jordanian Twist Quantization of D=4 Lorentz and Poincare Algebras and D=3 Contraction Limit
• Noncommutative Quantization for Noncommutative Field Theory
• Noncommutative Gravity and the *-Lie algebra of diffeomorphisms
• Quantum Deformations of Relativistic Symmetries

Cited by in corpus (7)

• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Three-dimensional gravity and Drinfel'd doubles: spacetimes and symmetries from quantum deformations
• Differential Structure on kappa-Minkowski Spacetime Realized as Module of Twisted Weyl Algebra
• Field Theory on Curved Noncommutative Spacetimes