Asymptotic Completeness for Compton Scattering
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''.
Cite
@article{arxiv.math-ph/0111032,
title = {Asymptotic Completeness for Compton Scattering},
author = {J. Froehlich and M. Griesemer and B. Schlein},
journal= {arXiv preprint arXiv:math-ph/0111032},
year = {2007}
}
Comments
gap of previous version closed, large parts rewritten, more general results and more comprehensive exposition. 64 pages, 3 figures