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Abstract

The high energy behavior of scattering amplitudes in spacetime dimensions,
$D>4$, is investigated. The bound on total cross sections, $\sigma_t \le
Constant~(los s)^{D-2}$, $D\ge 4$ has been obtained in the past under usual
assumptions. I derive new bound on scattering amplitudes in the region
$|t|<T_0$, $t$ being momentum transfer squared. and $T_0$ is a constant. The
existence of a zero-free region for the amplitude in complex t-plane, is
proved. I prove stronger upper and lower bounds for the absorptive amplitude in
the domain $0<t<T_0$.