Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-02-10
Physics
High Energy Physics
High Energy Physics - Theory
plain TeX with amssym and a few macros, 308 pages
Scientific paper
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 Poincar\'e group ${\cal P}_0$ on a differentiable manifold ${\cal U}_\infty$ 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 ${\cal U}_\infty$ at $t=0$. The existence of modified wave operators $\Omega_+$ and $\Omega_-$ and asymptotic completeness is proved. The asymptotic representations $U^{(\epsilon)}_g = \Omega^{-1}_\epsilon \circ U_g \circ \Omega_\epsilon$, $\epsilon = \pm$, $g \in {\cal P}_0$, turn out to be nonlinear. A cohomological interpretation of the results in the spirit of nonlinear representation theory and its connection to the infrared tail of the electron is given.
Flato Moshé
Simon Jacques C. H.
Taflin Erik
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