Complex Scalar Field

  • Thread starter mahnamahna
  • Start date
  • #1

Homework Statement


Derive the Feynman rules for for a complex scalar field.

Homework Equations


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


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].
294Kl.png

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:

Answers and Replies

Related Threads on Complex Scalar Field

  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
0
Views
815
Replies
1
Views
2K
  • Last Post
Replies
2
Views
972
  • Last Post
Replies
0
Views
1K
Replies
2
Views
740
Replies
2
Views
859
Replies
4
Views
2K
Replies
2
Views
1K
Replies
24
Views
579
Top