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Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory. II

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.