1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted