Jost-Lehmann-Dyson Representation and Froissart-Martin Bound in Quantum Field Theory on Noncommutative Space-Time
| dc.creator | Chaichian, M. | |
| dc.creator | Tureanu, A. | |
| dc.date | 2004-03-02 | |
| dc.date | 2004-10-08 | |
| dc.date.accessioned | 2026-07-07T04:16:41Z | |
| dc.date.available | 2026-07-07T04:16:41Z | |
| dc.description | In the framework of quantum field theory (QFT) on noncommutative (NC) space-time with $SO(1,1)\times SO(2)$ symmetry, which is the feature arising when one has only space-space noncommutativity ($θ_{0i}=0$), 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 $2\to 2$-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. | |
| dc.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/hep-th/0403032 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0403032 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/52456 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Jost-Lehmann-Dyson Representation and Froissart-Martin Bound in Quantum Field Theory on Noncommutative Space-Time | |
| dc.type | text |