Analyticity and Forward Dispersion Relations in Noncommutative Quantum Field Theory

Abstract

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. ${\theta }_{0i}=0$, 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, ${\theta }_{0i}\ne 0$, as well as on the nonforward scattering amplitude and mention their peculiarities.

28 pages, latex, no figures

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• Noncommutative Field Theory
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• Remarks on Time-Space Noncommutative Field Theories
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• Unitarity of Time-Like Noncommutative Gauge Theories: The Violation of Ward Identities in Time-Ordered Perturbation Theory
• On general properties of Lorentz invariant formulation of noncommutative quantum field theory
• Analyticity of the Scattering Amplitude, Causality and High-Energy Bounds in Quantum Field Theory on Noncommutative Space-Time
• (2+1)D Noncommutative CP${}^{N-1}$ Model
• Källén-Lehmann representation of noncommutative quantum electrodynamics
• Causality in Non-Commutative Quantum Field Theories
• Quantized Equations of Motion and Currents in Noncommutative Theories
• Jost-Lehmann-Dyson Representation, Analyticity in Angle Variable and Upper Bounds in Noncommutative Quantum Field Theory
• Rigorous results in space-space noncommutative quantum field theory