Dirac-Bergmann Constraints in Relativistic Physics: Non-Inertial Frames, Point Particles, Fields and Gravity

Abstract: There is a review of the physical theories needing Dirac-Bergmann theory of constraints at the Hamiltonian level due to the existence of gauge symmetries. It contains: i) the treatment of systems of point particles in special relativity both in inertial and non-inertial frames with a Wigner-covariant way of eliminating relative times in relativistic bound states; ii) the description of the electro-magnetic field in relativistic atomic physics and of Yang-Mills fields in absence of Gribov ambiguity in particle physics; iii) the identification of the inertial gauge variables and of the physical variables in canonical ADM tetrad gravity in presence of the electro-magnetic field and of charged scalar point particles in asymptotically Minkowskian space-times without super-translations by means of a Shanmugadhasan canonical transformation to a York canonical basis adapted to ten of the 14 first-class constraints and the definition of the Hamiltonian Post-Minkowskian weak field limit. Review paper for a chapter of a future book