Nonlinear and Quantum Origin of Doubly Infinite Family of Modified Addition Laws for Fourmomenta

Abstract

We show that infinite variety of Poincaré bialgebras with nontrivial classical r-matrices generate nonsymmetric nonlinear composition laws for the fourmomenta. We also present the problem of lifting the Poincaré bialgebras to quantum Poincaré groups by using e.g. Drinfeld twist, what permits to provide the nonlinear composition law in any order of dimensionfull deformation parmeter $\lambda$ (from physical reasons we can put $\lambda ={\lambda }_p$ where ${\lambda }_p$ is the Planck lenght). The second infinite variety of composition laws for fourmomentum is obtained by nonlinear change of basis in Poincaré algebra, which can be performed for any choice of coalgebraic sector, with classical or quantum coproduct. In last Section we propose some modification of Hopf algebra scheme with Casimir-dependent deformation parameter, which can help to resolve the problem of consistent passage to macroscopic classical limit.

LaTeX, 9 pages, Invited talk at 11-th International Colloqium "Quantum Groups and Integrable Systems", June 2002, Prague, presented by J. Lukierski; in press in Proceedings Volume of Czech. J. Phys. vol. 52, (2002)

References in corpus (5)

• Lorentz invariance with an invariant energy scale
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Doubly Special Relativity theories as different bases of $\kappa$--Poincaré algebra
• Deformed Boost Transformations That Saturate at the Planck Scale
• κ-deformations of D=4 Weyl and conformal symmetries

Cited by in corpus (8)

• New varying speed of light theories
• Scalar field propagation in the phi^4 kappa-Minkowski model
• On the definition of velocity in doubly special relativity theories
• A note on DSR-like approach to space-time
• Light-like $\kappa$-deformations and scalar field theory via Drinfeld twist
• Special relativity with two invariant scales: Motivation, Fermions, Bosons, Locality, and Critique
• Lorentz Symmetry and Ultra-High-Energy Cosmic Rays
• Twisting kappa-deformed phase space