Charged Particles and the Electro-Magnetic Field in Non-Inertial Frames of Minkowski Spacetime

TL;DR

This paper develops a comprehensive framework for describing charged particles and electromagnetic fields in non-inertial frames within Minkowski spacetime, including gauge transformations, Hamiltonian formulations, and astrophysical phenomena.

Contribution

It introduces a novel 3+1 Hamiltonian approach to non-inertial frames, extending inertial dynamics, and provides new insights into electromagnetic phenomena in accelerated reference frames.

Findings

Formulation of non-inertial Maxwell equations and Hamiltonian description.

Definition of non-inertial radiation gauge and Coulomb potential.

Analysis of astrophysical effects like wrap-up, Faraday rotation, and Sagnac effect.

Abstract

By using the 3+1 point of view and parametrized Minkowski theories we develop the theory of {\it non-inertial} frames in Minkowski space-time. The transition from a non-inertial frame to another one is a gauge transformation connecting the respective notions of instantaneous 3-space (clock synchronization convention) and of the 3-coordinates inside them. As a particular case we get the extension of the inertial rest-frame instant form of dynamics to the non-inertial rest-frame one. We show that every isolated system can be described as an external decoupled non-covariant canonical center of mass (described by frozen Jacobi data) carrying a pole-dipole structure: the invariant mass and an effective spin. Moreover we identify the constraints eliminating the internal 3-center of mass inside the instantaneous 3-spaces. In the case of the isolated system of positive-energy scalar particles with Grassmann-valued electric charges plus the electro-magnetic field we obtain both Maxwell equations and their Hamiltonian description in non-inertial frames. Then by means of a non-covariant decomposition we define the non-inertial radiation gauge and we find the form of the non-covariant Coulomb potential. We identify the coordinate-dependent relativistic inertial potentials and we show that they have the correct Newtonian limit. Then we study properties of Maxwell equations in non-inertial frames like the wrap-up effect and the Faraday rotation in astrophysics. Also the 3+1 description without coordinate-singularities of the rotating disk and the Sagnac effect are given, with added comments on pulsar magnetosphere and on a relativistic extension of the Earth-fixed coordinate system.