Optical theorem
= Optical theorem
Write the <S-matrix> as $S=1+iT$. <Unitarity> gives $-i(T-T^\dagger)=T^\dagger T$, so the diagonal forward matrix element obeys $2\operatorname{Im}T_{ii}=\sum_f\int d\Phi_f\,|T_{fi}|^2$. Thus the imaginary part of a forward <scattering amplitude> measures the total inclusive transition rate. For an electromagnetic source, the <hadronic electromagnetic-current spectral density> supplies the inclusive spectral sum.