# Complex Scalar Field

## Homework Statement

Derive the Feynman rules for for a complex scalar field.

## Homework Equations

$L=\partial_\mu\phi^\dagger\partial^\mu\phi +m^2\phi-\lambda/4 |\phi|^4$

## The Attempt at a Solution

I wrote the generating functional for the non-interacting theory
$Z_0[J]=Z_0[0]exp(-\int d^4xd^4yJ^\dagger (x) J(y) D_F(x-y)$

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 $-i\lambda\int d^4z$.

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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