  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 of Minkowski space and yields a strong form of locality valid
for all non-isotropic intervals if assumed true for space-like separations.
