 03504 J. Froehlich, M. Griesemer, B. Schlein
 Asymptotic Completeness for Compton Scattering
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Nov 17, 03

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Abstract. Scattering in a model of a massive quantummechanical particle, an
``electron'', interacting with massless, relativistic bosons,
``photons'', is studied. The interaction term in the Hamiltonian
of our model describes emission and absorption of ``photons'' by
the ``electron''; but ``electronpositron'' pair production is
suppressed. An ultraviolet cutoff and an (arbitrarily small, but
fixed) infrared cutoff are imposed on the interaction term. In a
range of energies where the propagation speed of the dressed
``electron'' is strictly smaller than the speed of light,
unitarity of the scattering matrix is proven, provided the
coupling constant is small enough; (asymptotic completeness of
Compton scattering). The proof combines a construction of dressed
oneelectron states with propagation estimates for the
``electron'' and the ``photons''.
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