Positivity of the real part of the forward scattering amplitude

TL;DR

This paper proves that the real part of the forward scattering amplitude remains positive at high energies under the condition that the total cross section increases monotonically to infinity.

Contribution

It establishes a general theorem linking the positivity of the real part of the amplitude to the monotonic increase of the total cross section at high energies.

Findings

Real part of the forward scattering amplitude is positive at high energies.

Positivity holds if the total cross section increases monotonically to infinity.

The theorem applies to two-body scattering processes.

Abstract

We prove the general theorem that the real part of the forward two-body scattering amplitude is positive at sufficiently high energies if, above a certain energy, the total cross section increases monotonically to infinity at infinite energy.