Asymptotic Completeness for Compton Scattering

Details Asymptotic Completeness for Compton Scattering Asymptotic Completeness for Compton Scattering

2001-11-17

arxiv.org/abs/math-ph/0111032v3

Physics

Mathematical Physics

gap of previous version closed, large parts rewritten, more general results and more comprehensive exposition. 64 pages, 3 fig

Scientific paper

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''.

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