2009/08/03 by David Alba, Luca Lusanna · 1 citation
Engineering · Physics and Astronomy · #Geophysics and Sensor Technology #Quantum and Classical Electrodynamics #Relativity and Gravitational Theory #gr-qc
paper · pdf · doi:10.1142/s021988781000394x
published as Int.J.Geom.Meth.Mod.Phys.7:33-93,2010 · This paper and the second one are an adaptation of arXiv 0812.3057 for publication on Int.J.Geom. Methods in Modern Phys. 77p
arxiv created 2009/08/03 · openalex publication_date 2010/02/01 · arxiv updated 2010/03/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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. In the second paper we will 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 will be given, with added comments on pulsar magnetosphere and on a relativistic extension of the Earth-fixed coordinate system.