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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’’.

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Correspondence to J. Fröhlich.

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Communicated by H. Spohn

Dedicated to Freeman Dyson on the occasion of his 80th birthday

Work partially supported by U.S. National Science Foundation grant DMS 01-00160.

Acknowledgement. We thank V. Bach for his hospitality at the University of Mainz, where part of this work was done, and we are indebted to Gian Michele Graf for pointing out a serious gap in an earlier version of this paper. We also thank one of the referees for pointing out many typos and some small errors.

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Fröhlich, J., Griesemer, M. & Schlein, B. Asymptotic Completeness for Compton Scattering. Commun. Math. Phys. 252, 415–476 (2004). https://doi.org/10.1007/s00220-004-1180-x

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Keywords

  • Neural Network
  • Statistical Physic
  • Complex System
  • Nonlinear Dynamics
  • Electron State