This paper shows that replacing a photon with a classical laser field can coherently boost QED cross-sections and improve their energy scaling, for example sigma_1->1 ~ (omega/m)^4 versus sigma_2->2 ~ (omega/m)^6.
On beam models and their paraxial approximation
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abstract
We derive focused laser pulse solutions to the electromagnetic wave equation in vacuum. After reproducing beam and pulse expressions for the well-known paraxial Gaussian and axicon cases, we apply the method to analyse a laser beam with Lorentzian transverse momentum distribution. Whilst a paraxial approach has some success close to the focal axis and within a Rayleigh range of the focal spot, we find that it incorrectly predicts the transverse fall-off typical of a Lorentzian. Our vector-potential approach is particularly relevant to calculation of quantum electrodynamical processes in weak laser pulse backgrounds.
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Coherent enhancement of QED cross-sections in electromagnetic backgrounds
This paper shows that replacing a photon with a classical laser field can coherently boost QED cross-sections and improve their energy scaling, for example sigma_1->1 ~ (omega/m)^4 versus sigma_2->2 ~ (omega/m)^6.