A theorem concerning the asymptotic behavior of forward elastic scattering amplitudes in relativistic theories is stated and proved. The assumptions made are (1) identical spinless particles interact via Gφ3 and λφ4 couplings; (2) a cutoff of the propagators is introduced; (3) the forward scattering amplitude satisfies a Bethe-Salpeter equation in the crossed channel; (4) the kernel of the equation is an arbitrary finite subset of the Feynman graphs which compose the exact kernel. The theorem states that under these assumptions, the forward scattering amplitude exhibits Regge behavior, i. e., A(s, 0) → sα + O (1) as s → ∞.
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James D. Bjorken (1964) studied this question.
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