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29 March 2024
 
  » arxiv » hep-th/0403032

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Jost-Lehmann-Dyson Representation and Froissart-Martin Bound in Quantum Field Theory on Noncommutative Space-Time
M. Chaichian ; A. Tureanu ;
Date 2 Mar 2004
Subject hep-th
AbstractIn the framework of quantum field theory (QFT) on noncommutative (NC) space-time with $SO(1,1) imes SO(2)$ symmetry, which is the feature arising when one has only space-space noncommutativity ($ heta_{0i}=0$), we prove that the Jost-Lehmann-Dyson representation, based on the causality condition usually taken in connection with this symmetry, leads to the mere impossibility of drawing any conclusion on the analyticity of the $2 o 2$-scattering amplitude in $cosTheta$, $Theta$ being the scattering angle. A physical choice of the causality condition rescues the situation and as a result an analog of Lehmann’s ellipse as domain of analyticity in $cosTheta$ is obtained. However, the enlargement of this analyticity domain to Martin’s ellipse and the derivation of the Froissart bound for the total cross-section in NC QFT is possible {it only} in the special case when the incoming momentum is orthogonal to the NC plane. This is the first example of a nonlocal theory in which the cross-sections are subject to a high-energy bound. For the general configuration of the direction of the incoming particle, although the scattering amplitude is still analytic in the Lehmann ellipse, no bound on the total cross-section has been derived. This is due to the lack of a simple unitarity constraint on the partial-wave amplitudes, which could be used in this case. High-energy upper bounds on the total cross-section, among others, are also obtained for an arbitrary flat (noncompact) dimension of NC space-time.
Source arXiv, hep-th/0403032
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