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Feynman diagrams for phi phi -> phi phi

  1. Oct 31, 2015 #1
    1. The problem statement, all variables and given/known data
    Compute the matrix element for the scattering process [tex] \phi \phi \to \phi \phi [/tex]

    2. Relevant equations
    The Lagrangian is given by
    [tex] L = \frac{1}{2} \partial_{\mu} \phi \partial^{\mu} \phi + \frac{\alpha}{2} \phi \partial_{\mu} \phi \partial^{\mu} \phi + \frac{\beta}{2} \phi^2 \partial_{\mu} \phi \partial^{\mu} \phi [/tex]

    3. The attempt at a solution
    At tree level I included a 4 legged vertex diagram + 3 diagrams with an internal line. Is this correct? I get a delta function with 4 momenta ( multiplied with other terms) + product of 2 delta functions with 3 momenta (multiplied with other terms) equal to the scattering implitude multipplied by a delta function of 4 momenta.

    Now my question is just what are the Feynman diagrams for the general process: [tex] \phi \phi \to \phi \phi [/tex]
     
  2. jcsd
  3. Oct 31, 2015 #2
    If we consider an other case where the interaction term looks like [tex] c_1 \phi^3 + c_2 \phi^4, [/tex] can one just sum up the feynman diagrams (for eg. tree level diagrams) for phi3 theory and phi4 theory to express the [tex] \phi \phi \to \phi \phi [/tex] scattering?
     
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