Towards Relativistic Atomic Physics and Post-Minkowskian Gravitational Waves

A review is given of the formulation of relativistic atomic theory, in which there is an explicit realization of the Poincare' generators, both in the inertial and in the non-inertial rest-frame instant form of dynamics in Minkowski space-time. This implies the need to solve the problem of the relativistic center of mass of an isolated system and to describe the transitions from different conventions for clock synchronization, namely for the identifications of instantaneous 3-spaces, as gauge transformations. These problems, stemming from the Lorentz signature of space-time, are a source of non-locality, which induces a spatial non-separability in relativistic quantum mechanics, with implications for relativistic entanglement. Then the classical system of charged particles plus the electro-magnetic field is studied in the framework of ADM canonical tetrad gravity in asymptotically Minkowskian space-times admitting the ADM Poincare' group at spatial infinity, which allows to get the general relativistic extension of the non-inertial rest frames of special relativity. The use of the York canonical basis allows to disentangle the tidal degrees of freedom of the gravitational field from the inertial ones. The York time is the inertial gauge variable describing the general relativistic remnant of the gauge freedom in clock synchronization. However now each solution of Einstein's equations dynamically determines a preferred notion of instantaneous 3-spaces. The linearization of this canonical formulation in the weak field approximation will allow to find Hamiltonian Post-Minkowskian gravitational waves with an asymptotic background and without Post-Newtonian expansion in non-harmonic 3-orthogonal gauges