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.
CITATION STYLE
Duplij, S., Goldin, G. A., & Shtelen, V. (2014). Conformal inversion and maxwell field invariants in four- and six-dimensional spacetimes. In Trends in Mathematics (Vol. 64, pp. 233–242). Springer International Publishing. https://doi.org/10.1007/978-3-319-06248-8_20
Mendeley helps you to discover research relevant for your work.