J. Froehlich, M. Griesemer, B. Schlein
Asymptotic Completeness for Compton Scattering
(896K, Postscript)

ABSTRACT.  Scattering in a model of a massive quantum-mechanical 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 ``electron-positron'' 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 
one--electron states with propagation estimates for the 
``electron'' and the ``photons''.