  All conformal correlation functions of 3 scalar primary operators are
constructed in an axiomatic way, relying only on conformal symmetry and
causality. The construction makes use of the R-product and its analyticity
properties in Minkowski momentum space. The R-product is completely determined
by a system of partial differential equations (the Ward identities for
conformal transformations) and a boundary condition (permutation symmetry), up
to an OPE coefficient. Wightman functions and time-ordered products are then
derived from the R-product using operator identities, and the Schwinger
function is recovered after a Wick rotation to Euclidean space. This
construction does not rely on the Fourier transform of position-space
correlation functions.
