2004/03/02 by Масуд Чайчиан, M. Chaichian, Chaichian, M. +3
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0403032
28 pages
openalex publication_date 2004/03/02 · arxiv created 2004/10/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the framework of quantum field theory (QFT) on noncommutative (NC) space-time with SO(1,1)× SO(2) symmetry, which is the feature arising when one has only space-space noncommutativity (θ0i=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→ 2-scattering amplitude in cosΘ, Θ 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 cosΘ 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.