Analyticity of the Scattering Amplitude, Causality and High-Energy Bounds in Quantum Field Theory on Noncommutative Space-Time

TL;DR

This paper investigates the analyticity properties of the 2-to-2 scattering amplitude in noncommutative quantum field theory, revealing limitations of causality-based methods and exploring high-energy bounds similar to Froissart-Martin bounds.

Contribution

It demonstrates that causality conditions in noncommutative QFT do not lead to conclusions about scattering amplitude analyticity and discusses potential high-energy bounds.

Findings

Causality conditions do not imply analyticity of the scattering amplitude.

The Jost-Lehmann-Dyson representation's limitations in noncommutative QFT.

Exploration of high-energy bounds analogous to Froissart-Martin bound.

Abstract

In the framework of quantum field theory (QFT) on noncommutative (NC) space-time with the symmetry group $O(1,1)\times SO(2)$, we prove that the Jost-Lehmann-Dyson representation, based on the causality condition 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 $\cos\Theta$, $\Theta$ being the scattering angle. Discussions on the possible ways of obtaining high-energy bounds analogous to the Froissart-Martin bound on the total cross-section are also presented.