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General Gauge Invariance Problem!

  1. May 31, 2013 #1

    I have to prove that the amplitude of the process

    [itex]\gamma \gamma \to W^+ W^- [/itex]

    does not depend on the gauge we will choose, [itex]R_{\xi}[/itex].

    So I use the most general expressions for the propagators and vertices. I find 5 diagrams. One that involves only the 4 fields and a vertex, 1 t and one u channel with a W boson as propagator and 1 t and 1 u where the propagator is a non-physical field [itex]\phi[/itex].

    I just sum up the last 4, since the first one does not depend on the [itex]\xi[/itex] parameter but then I am stuck since nothing seems to make the horrible expressions in such a way that there will be no gauge dependence in the end..

    Any help?
  2. jcsd
  3. Jun 2, 2013 #2
    What is this unphysical field? - A ghost? If it is, I don't see how you make the diagram. If it's some field I don't know, please elaborate.
  4. Jun 2, 2013 #3
    It is a goldstone boson coming around in the [itex]R_{\xi}[/itex] gauge. Actually it is the charged one.
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