Conformal inversion and Maxwell field invariants in four- and six-dimensional spacetimes
Abstract
Conformally compactified (3+1)-dimensional Minkowski spacetime may be identified with the projective light cone in (4+2)-dimensional spacetime. In the latter spacetime the special conformal group acts via rotations and boosts, and conformal inversion acts via reflection in a single coordinate. Hexaspherical coordinates facilitate dimensional reduction of Maxwell electromagnetic field strength tensors to (3+1) from (4 + 2) dimensions. Here we focus on the operation of conformal inversion in different coordinatizations, and write some useful equations. We then write a conformal invariant and a pseudo-invariant in terms of field strengths; the pseudo-invariant in (4+2) dimensions takes a new form. Our results advance the study of general nonlinear conformal-invariant electrodynamics based on nonlinear constitutive equations.
Keywords
Cite
@article{arxiv.1312.2280,
title = {Conformal inversion and Maxwell field invariants in four- and six-dimensional spacetimes},
author = {Steven Duplij and Gerald A. Goldin and Vladimir Shtelen},
journal= {arXiv preprint arXiv:1312.2280},
year = {2017}
}
Comments
10 pages, birkjour.cls, submitted for the Proceedings of the XXXIInd Workshop on Geometric Methods in Physics, (Bialowieza, Poland, July 2013), v2: minor improvements