2001/11/17 by J. Froehlich, M. Griesemer, Froehlich, J. +3
Mathematics · Physics and Astronomy · #81U99 #81V10 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:81U99 #msc:81V10
paper · pdf · doi:10.48550/arxiv.math-ph/0111032
gap of previous version closed, large parts rewritten, more general results and more comprehensive exposition. 64 pages, 3 figures
arxiv created 2003/07/26 · arxiv updated 2009/11/30
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''.