FROM KAPPA-POINCARE ALGEBRA TO KAPPA-LORENTZ QUASIGROUP - A DEFORMATION OF RELATIVISTIC SYMMETRY

We consider an algebraic ansatz for the class of nonlinear D=4 Poincare algebras and show that it contains only the quantum kappa-Poincare (real Hopf) algebras, obtained recently by the contraction of U(q)(O(3, 2)). We derive the explicit formulae for the finite kappa-Lorentz transformations generated by the realizations of the kappa-Poincare algebra in D=4 momentum space. These finite kappa-Lorentz transformations form a quasigroup, with generalized composition law of the boost parameters (rapidities). We consider further the (2s+1)-component field realizations with arbitrary spin s and their finite kappa-Lorentz transformations. For s=1/2 we obtain the kappa-covariant Dirac equation, derived from the finite kappa-Lorentz boost formula. After the coupling of the kappa-deformed Dirac equation to the electromagnetic potential we show that in the lowest order (linear) in m(el)/kappa the kappa-corrections to the hydrogen atom energy levels vanish but the value g=2 of the electron's magnetic moment is modified (g=2-->g=2[1+(m(el)/kappa)]. Finally the space-time description of kappa-relativistic fields is briefly discussed.