# Towards Relativistic Atomic Physics and Post-Minkowskian Gravitational Waves - General Relativity and Quantum Cosmology

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Abstract: A review is given of the formulation of relativistic atomic theory, in whichthere is an explicit realization of the Poincare- generators, both in theinertial and in the non-inertial rest-frame instant form of dynamics inMinkowski space-time. This implies the need to solve the problem of therelativistic center of mass of an isolated system and to describe thetransitions from different conventions for clock synchronization, namely forthe identifications of instantaneous 3-spaces, as gauge transformations. Theseproblems, stemming from the Lorentz signature of space-time, are a source ofnon-locality, which induces a spatial non-separability in relativistic quantummechanics, with implications for relativistic entanglement. Then the classicalsystem of charged particles plus the electro-magnetic field is studied in theframework of ADM canonical tetrad gravity in asymptotically Minkowskianspace-times admitting the ADM Poincare- group at spatial infinity, which allowsto get the general relativistic extension of the non-inertial rest frames ofspecial relativity. The use of the York canonical basis allows to disentanglethe tidal degrees of freedom of the gravitational field from the inertial ones.The York time is the inertial gauge variable describing the generalrelativistic remnant of the gauge freedom in clock synchronization. However noweach solution of Einstein-s equations dynamically determines a preferred notionof instantaneous 3-spaces. The linearization of this canonical formulation inthe weak field approximation will allow to find Hamiltonian Post-Minkowskiangravitational waves with an asymptotic background and without Post-Newtonianexpansion in non-harmonic 3-orthogonal gauges.

Author: ** Luca Lusanna INFN**

Source: https://arxiv.org/