Jost-Lehmann-Dyson representation, analyticity in the angular variable, and upper bounds in noncommutative quantum field theory

Abstract

We prove the existence of an analogue of the Jost-Lehmann-Dyson representation in noncommutative quantum field theory for the case where the noncommutativity affects only the spatial variables. Using this representation, we show that there is a certain class of elastic scattering amplitudes that have an analytic continuation to the complex cos ϑ plane with the Martin ellipse as the related analyticity domain. Using the analyticity in the angular variable and the unitarity as a basis, we establish an analogue of the Froissart-Martin bound for the total cross section in the noncommutative case.