Analyticity and Forward Dispersion Relations in Noncommutative Quantum Field Theory

We derive the analytical properties of the elastic forward scattering amplitude of two scalar particles from the axioms of the noncommutative quantum field theory. For the case of only space-space noncommutativity, i.e. $θ_{0i}=0$, we prove the dispersion relation which is similar to the one in commutative quantum field theory. The proof in this case is based on the existence of the analog of the usual microcausality condition and uses the Lehmann-Symanzik-Zimmermann (LSZ) or equivalently the Bogoliubov-Medvedev-Polivanov (BMP) reduction formalisms. The existence of the latter formalisms is also shown. We remark on the general noncommutative case, $θ_{0i}\neq0$, as well as on the nonforward scattering amplitude and mention their peculiarities.

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