Rationality of conformally invariant local correlation functions on compactified Minkowski space

TL;DR

This paper proves that under certain physical and symmetry conditions, the correlation functions in quantum field theory are rational functions, using conformal invariance and positivity principles in any spacetime dimension.

Contribution

It demonstrates that energy positivity, locality, and global conformal invariance imply the rationality of Wightman functions in all spacetime dimensions.

Findings

Rationality of Wightman functions follows from GCI, energy positivity, and locality.

Correlation functions can be viewed as sections over the compactified Minkowski space.

A strong form of locality applies to all non-isotropic intervals under GCI.

Abstract

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.