2008/12/16 by David Alba, Alba, David, Luca Lusanna +1
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Astrophysics (astro-ph) #Atomic Physics (physics.atom-ph) #Earthquake Detection and Analysis #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Sensor Technology #High Energy Physics - Theory (hep-th) #Relativity and Gravitational Theory #astro-ph #gr-qc #hep-th #physics.atom-ph
paper · pdf · doi:10.48550/arxiv.0812.3057
106 pAGES
arxiv created 2008/12/16 · openalex publication_date 2008/12/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · 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. 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.