The purpose of this work is to present and give full proofs of new original research results concerning integration of and scattering for the classical Maxwell-Dirac equations. These equations govern first quantized electrodynamics and are the starting point for a rigorous formulation of quantum electrodynamics. The presentation is given within the formalism of nonlinear group and Lie algebra representations, i.e. the powerful new approach to nonlinear evolution equations covariant under a group action. The authors prove that the nonlinear Lie algebra representation given by the manifestly covariant Maxwell-Dirac equations is integrable to a global nonlinear representation of the Poincar group on a differentiable manifold of small initial conditions. This solves, in particular, the small-data Cauchy problem for the Maxwell-Dirac equations globally in time. The existence of modified wave operators and asymptotic completeness is proved. The asymptotic representations (at infinite time) turn out to be nonlinear. A cohomological interpretation of the results in the spirit of nonlinear representation theory and its connection to the infrared tail of the electron are developed.

Introduction 
The nonlinear representation $T$ and spaces of differentiable vectors 
The asymptotic nonlinear representation 
Construction of the approximate solution 
Energy estimates and $L^2-L^infty$ estimates for the Dirac field 
Construction of the modified wave operator and its inverse 
Appendix

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