In Minkowski space, the conformal group does not preserve causality. Observables such as correlation functions are invariant under the conformal algebra, but not under the conformal group. As shown by Lüscher and Mack, it is possible to restore the invariance under the conformal group by extending the flat Minkowski space into a Lorentzian cylinder. The original Minkowski space is conformally equivalent to a region of the cylinder called a Poincaré patch. In the cylinder, global conformal transformations do not violate causality: instead, they can move points outside the Poincaré patch.