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The Scattering Matrix in Higher Orders

  • Walter Greiner
  • Joachim Reinhardt

Abstract

In Chap. 3 many scattering processes were calculated to the lowest nonvanishing order of perturbation theory. Because of the small value of the coupling constant α ≈ 1/137 the first term alone frequently gives reliable results. Within a satisfactory theory, however, one should be able to calculate the contributions of higher orders too. As we shall see in QED — and the same is true in all quantum field theories — this leads to characteristic difficulties: some of the “small corrections” become infinitely large! Surmounting this problem has been an essential step in the development of the theory. In what follows we shall discuss “renormalization” in the lowest nontrivial order of perturbation theory. The finite theory obtained in this way can then be applied to calculate measurable effects of vacuum fluctuations, i.e. the interaction with virtually created particles.

Keywords

Energy Shift Vacuum Polarization Renormalization Constant Lamb Shift Vertex Correction 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Walter Greiner
    • 1
    • 2
  • Joachim Reinhardt
    • 1
    • 2
  1. 1.Institut für Theoretische PhysikJohann Wolfgang Goethe-Universität FrankfurtFrankfurt am MainGermany
  2. 2.Frankfurt am MainGermany

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