Notes on Feynman Diagrams for Scattering Problems in One Dimension

Tomás A. Arias

Massachusetts Institute of Technology

Department of Physics

Physics 8.04 May 29, 1997

• Contents
• Introduction
• The Sum Over Histories
• Construction of Feynman Rules for One-Dimensional Scattering
  • Construction of Feynman Diagrams
  • Use of Feynman Diagrams to Prove General Theorems in Scattering Theory: Time Reversal and Parity
    • (*) Scattering amplitudes from mirror-image potentials
    • (*) Scattering of the same potential from two different directions: Time reversal symmetry
  • Application of Diagrams to Compute Scattering Amplitudes
  • Extracting the rules
  • General rules for all scattering problems in one dimension
  • (*) General Rules for Classically Forbidden Regions: Analytic Continuation
• Feynman Sums: two scattering centers
  • Analysis of the results: resonant scattering
  • Specific results for the barrier potential
• Three Nobel Ideas: Renormalization, Renormalization Group, Anderson Localization
  • Renormalization: Three scattering centers
  • Renormalization Group and Summing Uncountably Infinite Diagrams: An infinite crystal
  • Anderson Localization: Introduction of disorder
• Scattering from Smooth Potentials: WKB approximation
• About this document ...

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