CHARGED PARTICLES AND THE ELECTRO-MAGNETIC FIELD IN NONINERTIAL FRAMES OF MINKOWSKI SPACE-TIME I: ADMISSIBLE 3 + 1 SPLITTINGS OF MINKOWSKI SPACE-TIME AND THE NONINERTIAL REST FRAMES

Abstract

By using the 3 + 1 point of view and parametrized Minkowski theories we develop the theory of noninertial frames in Minkowski space-time. The transition from a noninertial frame to another one is a gauge transformation connecting the respective notions of instantaneous three-space (clock synchronization convention) and of the three-coordinates inside them. As a particular case we get the extension of the inertial rest-frame instant form of dynamics to the noninertial rest-frame one. We show that every isolated system can be described as an external decoupled noncovariant 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 three-center of mass inside the instantaneous three-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 noninertial frames. Then by means of a noncovariant decomposition we define the noninertial radiation gauge and we find the form of the noncovariant 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 noninertial 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.