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Complex Scalar Field 
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#1
Oct2511, 01:32 AM

P: 6

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 noninteracting theory [itex]Z_0[J]=Z_0[0]exp(\int d^4xd^4yJ^\dagger (x) J(y) D_F(xy)[/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]. 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? 


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