  A new method for computing exact conformal partial wave expansions is
developed and applied to approach the problem of Hilbert space (Wightman)
positivity in a non-perturbative four-dimensional quantum field theory model.
The model is based on the assumption of global conformal invariance on
compactified Minkowski space. Bilocal fields arising in the harmonic
decomposition of the operator product expansion prove to be a powerful
instrument in exploring the field content. In particular, in the theory of a
field of dimension 4 which has the properties of a (gauge invariant)
Lagrangian, the scalar field contribution to the 6-point function of the twist
2 bilocal field is analyzed with the aim to separate the free field part from
the nontrivial part.
