Extension of relativistic mechanics by maximum symmetry group of Maxwell equations
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia 119991,
2 Faculty “Information Technologies and Applied Mathematics”, Moscow Aviation Institute (National Research University), Moscow, Russia 125993,
* e-mail: firstname.lastname@example.org
Accepted: 1 April 2020
Published online: 27 April 2020
Relativistic mechanics historically arose as a generalization of classical mechanics, which is consistent with the symmetries of the equations of electrodynamics by the use of the Lorentz and Poincare transforms instead of Galileo transformations. However, the Lorentz and Poincare groups are not maximal symmetry groups of the Maxwell equations, even if we restrict ourselves to local transformations of coordinates and time. In this paper, we propose a formulation of relativistic mechanics that is consistent with the group of maximal local symmetries of the Maxwell equations. We take into account dilations and geometric inversions in Minkowski space in addition to the Poincare and Lorentz transformations. The proposed most general form of relativistic mechanics, which is consistent with electrodynamics, is constructed using coordinate and time transformations from the conformal group C(1, 3). Equations of extended relativistic dynamics are proposed.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2020