Introduction.- Interaction of Electrons with Laser Fields.- Nonlinear Single Compton Scattering.- Nonlinear Double Compton Scattering.- Numerical Integration of Strongly Oscillating Functions.- Summary and Outlook.- Appendix A Differential Probability.- Appendix B The Dirac Equation.- Appendix C Quantum Scattering off a Focussed Beam.- Appendix D Asymptotic Limits of Nonlinear Single Compton Scattering.- Appendix E Asymptotic Limits of Nonlinear Double Compton Scattering.
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