Abstract: In this monograph we prove that the nonlinear Lie algebra representation
given by the manifestly covariant Maxwell-Dirac (M-D) equations is integrable to a global
nonlinear representation U of the Poincare group Vo on a differentiable manifold UQQ of
small initial conditions for the M-D equations. This solves, in particular, the Cauchy
problem for the M-D equations, namely existence of global solutions for initial data in
Uoo at t = 0. The existence of modified wave operators Q+ and ft- and asymptotic
completeness is proved. The asymptotic representations Ug = ft~x o Ug o ft£, e = ±,
g G Vo, 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 is given.
Received by the editor February 16, 1995, and in revised form May 13, 1996.
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