Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-09-02
Czech.J.Phys. 52 (2002) 1261-1268
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 9 pages, Invited talk at 11-th International Colloqium "Quantum Groups and Integrable Systems", June 2002, Prague, pres
Scientific paper
10.1023/A:1021393105890
We show that infinite variety of Poincar\'{e} bialgebras with nontrivial classical r-matrices generate nonsymmetric nonlinear composition laws for the fourmomenta. We also present the problem of lifting the Poincar\'{e} bialgebras to quantum Poincar\'{e} 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 Poincar\'{e} 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.
Lukierski Jerzy
Nowicki Anatol
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