CLASSICAL AND QUANTUM-MECHANICS OF FREE KAPPA-RELATIVISTIC SYSTEMS

We consider the Hamiltonian and Lagrangian formalism describing free kappa-relativistic particles with their four-momenta constrained to the kappa-deformed mass shell. We study the formalism with commuting as well as noncommuting (i.e., with nonvanishing Poisson brackets) space-time coordinates; in particular a kappa-deformed phase space formalism leading to the kappa-deformed covariant Heisenberg algebra is presented. We also describe the dependence of the formalism on the various definitions of the energy operator corresponding to different choices of basic generators in the kappa-deformed PoincarO algebra. The quantum mechanics of free kappa-relativistic particles and of the free kappa-relativistic oscillator are also presented. It is shown that the kappa-relativistic oscillator describes a quantum statistical ensemble with a finite value of the Hagedorn temperature. The relation to a kappa-deformed Schrodinger quantum mechanics in which the time derivative is replaced by a finite difference is also discussed. (C) 1995 Academic Press, Inc.