A Classical and Quantum Relativistic Interacting Variable-Mass Model

Luca Lusanna

R. P. Gaida, Tretyak, Yurij Yaremko

Collective center-of-mass variables are introduced in the Lagrangian formalism of the relativistic classical mechanics of directly interacting particles.It is shown that the transition to the Hamiltonian formalism leads to the Bakamjian-Thomas model.The quantum-mechanical system consisting of two spinless particles is investigated.Quasi-relativistic corrections to the discrete energy spectrum are calculated for some Coulomb-like interactions having field theoretical analogues.

Luca Lusanna

A review is given of a new relativistic classical mechanics for N-particle systems compatible with relativistic bound states. It is formulated in global non-inertial frames in Minkowski space-time by means of parametrized Minkowski theories and then restricted to the intrinsic inertial rest frame of the isolated system. There is a complete control on the relativistic collective variables (Newton-Wigner center of mass, Fokker-Pryce center of inertia, M/oller center of energy) and on the realization of the Poincare' algebra (with the explicit form of the interaction-dependent Lorentz boosts). The particle world-lines are found to correspond to the ones of predictive mechanics and localization problems are clarified. The model can be consistently quantized avoiding the instantaneous spreading of the center-of-mass wave packets (Hegerfeldt theorem), because the non-local non-covariant center of mass is a non-measurable quantity. This implies that the Hilbert space must be the tensor product of the center-of-mass Hilbert space with the one of relative motions. This spatial non-separability (due to the Lorentz signature of space-time) makes relativistic entanglement much more involved than the non-relativistic one.

Jan Rzewuski

Gerard ’t Hooft

Relativistic, scalar particles are considered, contained in a box with periodic boundary conditions. Although interactions are not expected to be a fundamental problem, we concentrate on free particles. By considering them to be harmonic oscillators, it is found that their dynamical variables can be replaced by a completely ontological set, which means that, here, quantum mechanics does not deviate from a purely geometric, ontological particle system. The effects of the mass terms are included. Locality holds for the quantum theory, and seems to be fully obeyed also by the classical treatment, although further discussion will be needed. Quantised interactions are briefly speculated on, but mostly postponed to later. We do discuss extensively the distinction between the quantum treatment and the classical one, even though they produce exactly the same equations mathematically. We briefly explain how this result can be squared with the usual quantum no-go theorems. It is suggested to apply this theory for real time quantum model simulations.

Hiroshi Enatsu