Cutting rules for strong-field QED are formulated and used to relate higher-loop corrections to trident pair production, yielding a spin-resolved analytical rate expression in constant crossed fields.
A brief Introduction to Dispersion Relations and Analyticity
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abstract
In these lectures we provide a basic introduction into the topic of dispersion relation and analyticity. The properties of 2-point functions are discussed in some detail from the viewpoint of the K\"all\'en-Lehmann and general dispersion relations. The Weinberg sum rules figure as an application. The analytic structure of higher point functions in perturbation theory are analysed through the Landau equations and the Cutkosky rules.
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Nonlocal Källén-Lehmann spectral densities in the Higgs sector yield exponentially suppressed scattering amplitudes above Λ_NL and suppress the real part of the Higgs self-energy at p² ~ -Λ²_NL, solving the hierarchy problem and testable via LHC global fits.