The optical theorem is a fundamental concept in quantum mechanics and particularly in the field of scattering theory. It establishes a relationship between the total cross section of a scattering process and the forward scattering amplitude. In more detail, the optical theorem states that the imaginary part of the forward scattering amplitude (the amplitude for scattering at an angle of zero) is proportional to the total cross section for that scattering process.
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Write the S-matrix as . Unitarity gives , so the diagonal forward matrix element obeys . 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.