Rationality of conformally invariant local correlation functions on compactified Minkowski space

Rationality of the Wightman functions is proven to follow from energy positivity, locality and a natural condition of global conformal invariance (GCI) in any number D of space-time dimensions. The GCI condition allows to treat correlation functions as generalized sections of a vector bundle over the compactification /line M of Minkowski space M and yields a strong form of locality valid for all non-isotropic intervals if assumed true for space-like separations. (orig.)