ASYMPTOTIC COMPLETENESS, GLOBAL EXISTENCE AND THE INFRARED PROBLEM FOR THE MAXWELL-DIRAC-EQUATIONS

In this monograph we prove that the nonlinear Lie algebra representati on given by the manifestly covariant Maxwell-Dirac (M-D) equations is integrable to a global nonlinear representation U of the Poincare grou p P-0 on a differentiable manifold U-infinity of small initial conditi ons for the M-D equations. This solves, in particular, the Cauchy prob lem for the M-D equations, namely existence of global solutions for in itial data in U-infinity at t=0. The existence of modified wave operat ors Omega(+) and Omega(-) and asymptotic completeness is proved. The a symptotic representations U-g((epsilon))=Omega(epsilon)(-1) circle U-g circle Omega(epsilon), epsilon=+/-, g is an element of P-0, turn out to be nonlinear. A cohomological interpretation of the results in the spirit of nonlinear representation theory and its connection to the in frared tail of the electron is given.