  Classical results of the axiomatic quantum field theory, namely the
irreducibility of the set of field operators, Reeh and Schlieder's theorems and
generalized Haag's theorem, are proven in $SO(1,1)$ invariant quantum field
theory, of which an important example is noncommutative quantum field theory.
New consequences of generalized Haag's theorem are obtained in $SO(1,3)$
invariant theories. It has been proven 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.
