  The most general operator product expansion in conformal field theory is
obtained using the embedding space formalism and a new uplift for general
quasi-primary operators. The uplift introduced here, based on quasi-primary
operators with spinor indices only and standard projection operators, allows a
unified treatment of all quasi-primary operators irrespective of their Lorentz
group irreducible representations. This unified treatment works at the level of
the operator product expansion and hence applies to all correlation functions.
A very useful differential operator appearing in the operator product expansion
is established and its action on appropriate products of embedding space
coordinates is explicitly computed. This computation leads to tensorial
generalizations of the usual Exton function for all correlation functions.
Several important identities and contiguous relations are also demonstrated for
these new tensorial functions. From the operator product expansion all
correlation functions for all quasi-primary operators, irrespective of their
Lorentz group irreducible representations, can be computed recursively in a
systematic way. The resulting answer can be expressed in terms of tensor
structures that carry all the Lorentz group information and linear combinations
of the new tensorial functions. Finally, a summary of the well-defined rules
allowing the computation of all correlation functions constructively is
presented.
