Rational conformal field theory in four-dimensional space-time

The recently established rationality of correlation functions in the globally conformal-invariant quantum field theory complying with the Whitman axioms is applied for plotting the family of the models solved in the Minkowski four- dimensional space-time. The model of the neutral scalar field φ of the 2 dimensionality is considered in detail. It depends on the positive material parameter c, the analogue of the Virasoro central charge, and by all (finite) c it provides for the infinite number of retained symmetrical tensor currents. It is shown that the algebra of the φ-field operator products coincides with the simpler algebra produced by the bilocal scalar field V (x1, x2) of the 1 + 1-dimensionality. The V modes together with a single operator produce the infinite Lie algebra, the vacuum (i.e. the lower weight with the zero energy) representations whereof depend only on the central charge c. It is proved that Whitman positivity (i.e. the unitarity of the algebra Lie presentations) is equivalent to the conditions c is an element of N