Complex Scalar Field

  1. 1. The problem statement, all variables and given/known data
    Derive the Feynman rules for for a complex scalar field.

    2. Relevant equations
    [itex]L=\partial_\mu\phi^\dagger\partial^\mu\phi +m^2\phi-\lambda/4 |\phi|^4[/itex]


    3. The attempt at a solution
    I wrote the generating functional for the non-interacting theory
    [itex]Z_0[J]=Z_0[0]exp(-\int d^4xd^4yJ^\dagger (x) J(y) D_F(x-y)[/itex]

    And I think I can use this to calculate the correlation functions directly, I just don't understand exactly how the presence of antiparticles change the Feynman diagrams/rules. I guess charge has to be conserved at all vertices, but I don't explicitly see that condition (I see overall charge conservation). Is this the only change in the Feynman rules? The propagators for both seem the same, and each vertex still gives [itex]-i\lambda\int d^4z[/itex].
    [​IMG]
    These pictures contribute to different 4 point functions, but do they contribute the same term to their respective sums? Also, does the presence of anti particles change the calculation of symmetry factors?
     
    Last edited: Oct 25, 2011
  2. jcsd
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