  Recently established rationality of correlation functions in a globally
conformal invariant quantum field theory satisfying Wightman axioms is used to
construct a family of soluble models in 4-dimensional Minkowski space-time. We
consider in detail a model of a neutral scalar field $\phi$ of dimension 2. It
depends on a positive real parameter c, an analogue of the Virasoro central
charge, and admits for all (finite) c an infinite number of conserved symmetric
tensor currents. The operator product algebra of $\phi$ is shown to coincide
with a simpler one, generated by a bilocal scalar field $V(x_1,x_2)$ of
dimension (1,1). The modes of V together with the unit operator span an
infinite dimensional Lie algebra $L_V$ whose vacuum (i.e. zero energy lowest
weight) representations only depend on the central charge c. Wightman
positivity (i.e. unitarity of the representations of $L_V$) is proven to be
equivalent to $c \in N$.
