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Abstract

We consider a massive, neutral, scalar field theory of mass $m_0$ in a five
dimensional flat spacetime. Subsequently, one spatial dimension is compactified
on a circle, $S^1$, ofradius $R$. The resulting theory is defined in the
manifold, $R^{3,1}\otimes S^1$. The mass spectrum is a state of lowest mass,
$m_0$, and a tower of massive Kaluza-Klein states. The analyticity property of
the elastic scattering amplitude is investigated in the
Lehmann-Symanzik-Zimmermann (LSZ) formulation of this theory. In the context of
nonrelativistic potential scattering, for the $R^3\otimes S^1$ spatial
geometry, it was shown that the forward scattering amplitude does not satisfy
analyticity properties in some cases for a class of potentials. If the same
result is valid in relativistic quantum field theory then the consequences will
be far reaching. We show that the forward elastic scattering amplitude of the
theory, in the LSZ axiomatic approach, satisfies forward dispersion relations.
The importance of the unitarity constraint on the S-matrix, is exhibited in
displaying the properties of the absorptive part of the amplitude.