 00276 Dimitri YAFAEV, Yannick GATEL.
 Scattering theory for the Dirac operator with a longrange electromagnetic
potential.
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Jun 20, 00

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Abstract. We consider the Dirac operator with a longrange
potential $V(x)$. Scalar, pseudoscalar and vector components of
$V(x)$ may have arbitrary powerlike decay at infinity. We
introduce wave operators with timeindependent modifiers. These
modifiers are pseudodifferential operators whose symbols are,
roughly speaking, constructed in terms of approximate
eigenfunctions of the stationary problem. We derive and solve
eikonal and transport equations for the corresponding phase and
amplitude functions. From analytical point of view, our proof of
the existence and completeness of the wave operators relies on the
limiting absorption principle and radiation estimates established
in the paper. This allows us to fit the longrange scattering
theory for the Dirac operator into the framework of smooth
perturbations. Finally, we find the asymptotics for large times
$t$ of solutions $u(x,t)$ of the timedependent Dirac equation.
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