Abstract
We consider a massive scalar, neutral, field theory in a five dimensional flat spacetime. Subsequently, one spatial dimension is compactified on a circle, S1, of radius R. The resulting theory is defined in the manifold, R3,1⊗S1, consists of a states of lowest mass, m0, and a tower of massive Kaluza-Klein states. The analyticity property of the elastic scattering amplitude is investigated in the frame works of Lehmann-Symanzik-Zimmermann formulation of this field theory. In the context of nonrelativistic potential scattering, for R3⊗S1 spatial geometry, it was shown that the forward scattering amplitude does not satisfy analyticity for a class of potentials which might have important consequences if same attribute holds in relativistic quantum field theories. We address this issue with R3,1⊗S1 geometry. We show that the forward scattering amplitude of the theory satisfying LSZ axioms does not suffer from lack of analyticity. The importance of the unitarity constraint is exhibited in displaying the properties of the absorptive part of the forward amplitude.
Highlights
The analyticity property of scattering amplitude is a cardinal attribute and this has been derived in the frameworks of general relativistic quantum field theories.The scattering amplitude, F (s, t), is an analytic function of the center of mass energy squared, s, for momentum transfer squared, t
Our principal goal of this article is to study the analyticity property of the forward scattering amplitude for a five dimensional scalar field theory which is compactified to R3,1 ⊗ S1
There were some concerns if dispersion relation is invalidated in relativistic quantum field theories
Summary
The analyticity property of scattering amplitude is a cardinal attribute and this has been derived in the frameworks of general relativistic quantum field theories. It was shown by Khuri [23], through counter examples, within the framework of perturbation theory, how the analyticity of the forward scattering amplitude breaks down in the presence of S1 compactification for a class of nonrelativistic potential models under certain circumstances as we shall describe later The purpose of this investigation is to study the analyticity properties of the scattering amplitude in a field theory with an S1 compactified spatial dimension. Khuri noted an important feature of his studies that in the case when scattering theory was applied perturbatively in R3 space the resulting amplitude satisfied analyticity properties for similar Yukawa-type potentials [19, 20]. We shall keep this aspect in mind and we shall undertake a systematic study of the analyticity of scattering amplitude in the sequel
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