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

## TL;DR

This paper reviews the application of Dirac-Bergmann constraint theory across various relativistic physical systems, including particles, fields, and gravity, emphasizing gauge variables and Hamiltonian formulations in different frames.

## Contribution

It provides a comprehensive analysis of Dirac-Bergmann constraints in relativistic physics, introducing new methods for gauge fixing and variable identification in complex systems.

## Key findings

- Elimination of relative times in relativistic bound states.
- Description of electromagnetic and Yang-Mills fields without Gribov ambiguity.
- Identification of physical variables in ADM tetrad gravity with charged particles.

## 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