On relativistic quantum mechanics in the rest-frame instant form of dynamics

8th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields

Lusanna, Luca^1

Sezione INFN di Firenze, Via Sansone 1, 50019 Sesto Fiorentino (FI), Italy^1

关键词: Center of inertias;    Classical mechanics;    Collective variables;    Complete control;    Localization problems;    Minkowski space-time;    Non-inertial frame;    Relativistic quantum mechanics;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/437/1/012015/pdf
DOI  :  10.1088/1742-6596/437/1/012015

来源: IOP

【 摘 要 】

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.