Special conformal transformation

A special conformal transformation can be written[1] It is a composition of an inversion (xμ → xμ/x2 = yμ), a translation (yμ → yμ − bμ = zμ), and another inversion (zμ → zμ/z2 = x′μ) Its infinitesimal generator is Special conformal transformations have been used to study the force field of an electric charge in hyperbolic motion.

Homographies on P(B) include translations: The homography group G(B) includes of translations at infinity with respect to the embedding q → U(q:1); The matrix describes the action of a special conformal transformation.

[4] The translations form a subgroup of the linear fractional group acting on a projective line.

The translations at infinity thus form another subgroup of the homography group on the projective line.

The term special conformal transformation ("speziellen konformen Transformationen" in German) was first used in 1962 by Hans Kastrup.