Conformal-Invariant Green Functions Without Ultraviolet Divergences

It is known that conformal invariance, with anomalous dimensions, determines the 2- and 3-point functions in relativistic quantum field theory up to some constants. It is then natural to use these to construct the skeleton-graph expansion of the general $n$-point Green function. We demonstrate that this leads to well-defined conformal-invariant expressions, for non-exceptional external momenta, given by ordinary convergent (Riemann) integrals. This also applies to the integrals in the Schwinger-Dyson equation for the 2- and 3-point functions. These results support in particular conjectures recently advanced by Migdal—including self-consistency of conformal invariance. All results are derived for (pseudo-) scalar Yukawa theory.