# Nonlinear and quantum origin of doubly infinite family of modified addition laws for fourmomenta

@article{Lukierski2002NonlinearAQ,
title={Nonlinear and quantum origin of doubly infinite family of modified addition laws for fourmomenta},
author={Jerzy Lukierski and Anatol Nowicki},
journal={Czechoslovak Journal of Physics},
year={2002},
volume={52},
pages={1261-1268}
}
• Published 2 September 2002
• Mathematics
• Czechoslovak Journal of Physics
We show that infinite variety of Poincaré bialgebras with nontrivial classicalr-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 parameterλ (from physical reasons we can putλ=λp whereλp is the Planck length). The second infinite variety of composition…
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## References

SHOWING 1-10 OF 36 REFERENCES

• Mathematics
• 1994
We consider the twisting of the Hopf structure for the classical enveloping algebra U(g), where g is an inhomogenous rotation algebra, with explicit formulae given for the D=4 Poincare algebra
• Physics
• 1993
We consider the Hamiltonian and Lagrangian formalism describing free κ-relativistic particles with their four-momenta constrained to the κ-deformed mass shell. We study the formalism with commuting
• Mathematics
• 1993
This thesis consists of four papers. In the first paper we present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. Under certain conditions
• Mathematics
• 1999
Jordanian quantizations of Lie algebras are studied using the factorizable twists. For a restricted Borel subalgebra B∨ of sl(N) the explicit expressions are obtained for the twist element F,
• Mathematics
• 1994
The kappa-deformed D=4 Poincare superalgebra written in Hopf superalgebra form is transformed to the basis with classical Lorentz subalgebra generators. We show that in such a basis the
• Mathematics
• 1994
We present here the general solution describing generators of \kdef \poin algebra as the functions of classical \poin algebra generators as well as the inverse formulae. Further we present analogous
• Physics, Mathematics
• 1963
Relativistic invariance may involve two different theoretical postulates: symmetry of the theory under the relativistic transformation group reflecting the invariance of physical laws under changes
Introduction 1. Definition of Hopf algebras 2. Quasitriangular Hopf algebras 3. Quantum enveloping algebras 4. Matrix quantum groups 5. Quantum random walks and combinatorics 6. Bicrossproduct Hopf