  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.
