# Charged Particles and the Electro-Magnetic Field in Non-Inertial Frames of Minkowski Spacetime: I. Admissible 3 1 Splittings of Minkowski Spacetime and the Non-Inertial Rest Frames - General Relativity and Quantum Cosmology

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Abstract: By using the 3+1 point of view and parametrized Minkowski theories we developthe theory of {\it non-inertial} frames in Minkowski space-time. The transitionfrom a non-inertial frame to another one is a gauge transformation connectingthe respective notions of instantaneous 3-space clock synchronizationconvention and of the 3-coordinates inside them. As a particular case we getthe extension of the inertial rest-frame instant form of dynamics to thenon-inertial rest-frame one. We show that every isolated system can bedescribed as an external decoupled non-covariant canonical center of massdescribed by frozen Jacobi data carrying a pole-dipole structure: theinvariant mass and an effective spin. Moreover we identify the constraintseliminating the internal 3-center of mass inside the instantaneous 3-spaces. Inthe case of the isolated system of positive-energy scalar particles withGrassmann-valued electric charges plus the electro-magnetic field we obtainboth Maxwell equations and their Hamiltonian description in non-inertialframes. Then by means of a non-covariant decomposition we define thenon-inertial radiation gauge and we find the form of the non-covariant Coulombpotential. We identify the coordinate-dependent relativistic inertialpotentials and we show that they have the correct Newtonian limit. In thesecond paper we will study properties of Maxwell equations in non-inertialframes like the wrap-up effect and the Faraday rotation in astrophysics. Alsothe 3+1 description without coordinate-singularities of the rotating disk andthe Sagnac effect will be given, with added comments on pulsar magnetosphereand on a relativistic extension of the Earth-fixed coordinate system.

Autor: David Alba, Luca Lusanna

Fuente: https://arxiv.org/