세리자와

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  1. Solition in sine-Gordon theory
    1. What is the solition?
      1. Definition: Localized travelling wave solutions of the non-linear equation.(ex Kinks, but ...) Scattering condition (maybe mentioned together w/ sine-Gordon solitons).
    2. Single and multi solition solutions of sine-Gordon theory
      1. There are exact exact solition soutions (w/ pictures)
      2. They have topological charges
      3. Time delay and inter-soliton force
        1. Time delay as the residual effect of collision (may write down the asymptotic form and the actual time delays)
      4. Doublet as the bound state
        1. Doublet periods (masses) are quantized
        2. The lowest doublet is the elementary boson (up to two loop)
          1. May comment why the one-loop matches with two loops
  2. Metamorphosis
    1. Fermions in 2d (briefly, how many components, Gamma matrices)
    2. Metamorphosis for free theories
      1. OPE of e^(iax) and fermions
      2. Mapping between constants
      3. From fermions to bosons
    3. Metamorphosis for the sine-Gordon theory
      1. Mandelstam's soliton operators
        1. Define soliton operators
        2. Commutation relations. To be fermions or not to be (minimal derivations. will have done it actually)
        3. Soliton operator satisfies the massive Thirring equation
  3. Conclusion - Solitons are fermions!


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