Jost-Lehmann-Dyson Representation, Analyticity in Angle Variable and Upper Bounds in Noncommutative Quantum Field Theory

TL;DR

This paper proves an analogue of the Jost-Lehmann-Dyson representation in noncommutative quantum field theory, establishing analyticity properties of scattering amplitudes and deriving an upper bound on total cross sections.

Contribution

It introduces a noncommutative analogue of the Jost-Lehmann-Dyson representation and derives Froissart-Martin bounds in this framework.

Findings

Analytic continuation of elastic amplitudes into the complex cosine plane.

Establishment of the Martin ellipse domain of analyticity.

Derivation of Froissart-Martin upper bound on total cross section.

Abstract

The existence of Jost-Lehmann-Dyson representation analogue has been proved in framework of space-space noncommutative quantum field theory. On the basis of this representation it has been found that some class of elastic amplitudes admits an analytical continuation into complex \cos\vartheta plane and corresponding domain of analyticity is Martin ellipse. This analyticity combined with unitarity leads to Froissart-Martin upper bound on total cross section.