Geometry of attosecond laser pulses and photon-photon scattering at high energies

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We derive the total cross section for scattering of a photon on an ultra-short laser pulse at high energies. We take into account all multi-photon interactions. We argue that the nonlinear effects due to these interactions become important at very high intensities of the laser pulse. We demonstrate however, that these intensities are significantly lower than the Schwinger critical value.