Communications in Mathematical Physics

, Volume 252, Issue 1–3, pp 415–476 | Cite as

Asymptotic Completeness for Compton Scattering

  • J. FröhlichEmail author
  • M. Griesemer
  • B. Schlein


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’’.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Electron State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Theoretical Physics, ETH–HönggerbergZürichSwitzerland
  2. 2.Department of MathematicsUniversity of Alabama at BirminghamBirminghamUSA
  3. 3.Department of MathematicsStanford UniversityStanfordCAUSA

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