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''.