Holography and the Future Tube

The Future Tube $T^+_n$ of n-dimensional Minkowski spacetime may be identified with the reduced phase space or "space of motions" of a particle moving in (n+1)-dimensional Anti-de-Sitter spacetime. Both are isomorphic to a bounded homogeneous domain in ${\bf C}^{n}$ whose Shilov boundary may be identified with $n$-dimensional conformally compactified Minkowski spacetime.