CLASSICAL AND QUANTUM-MECHANICS OF FREE KAPPA-RELATIVISTIC SYSTEMS

We consider the Hamiltonian and Lagrangian formalism describing free k appa-relativistic particles with their four-momenta constrained to the kappa-deformed mass shell. We study the formalism with commuting as w ell as noncommuting (i.e., with nonvanishing Poisson brackets) space-t ime coordinates; in particular a kappa-deformed phase space formalism leading to the kappa-deformed covariant Heisenberg algebra is presente d. We also describe the dependence of the formalism on the various def initions of the energy operator corresponding to different choices of basic generators in the kappa-deformed PoincarO algebra. The quantum m echanics of free kappa-relativistic particles and of the free kappa-re lativistic oscillator are also presented. It is shown that the kappa-r elativistic oscillator describes a quantum statistical ensemble with a finite value of the Hagedorn temperature. The relation to a kappa-def ormed Schrodinger quantum mechanics in which the time derivative is re placed by a finite difference is also discussed. (C) 1995 Academic Pre ss, Inc.