  Generalized Haag's theorem has been proved in S O (1, k) invariant quantum
field theory. Apart from the above mentioned k+1 variables there can be
arbitrary number of additional coordinates including noncommutative ones in the
theory. New consequences of generalized Haag's theorem are obtained. It has
been proved that the equality of four-point Wightman functions in two theories
leads to the equality of elastic scattering amplitudes and thus the total
cross-sections in these theories. In space-space noncommutative quantum field
theory in four-dimensional case it has been proved that if in one of the
theories under consideration S-matrix is equal to unity, then in another theory
S-matrix is unity as well.
