Scalar field EM interaction vertices

[JonathanApps]

The Lagrangian for a scalar field (eg charged pions) interacting with an EM field is roughly

 

(\partial_{\mu}\phi - e A_{\mu}\phi)(\partial^{\mu}\phi - e A^{\mu}\phi) + m^2 \phi^2

 

or something like that, for charge e.

 

So my question is: one term in this is proportional to \phi\phi\ A^2. So do we get Feynman graphs with 4 lines

(2 pion, 2 photon) leading to one vertex?

 

I've never seen a graph like that and it seems odd. I've also never heard anyone mention them. Do we get them or am I missing something (i.e. these 4-point vertices somehow disappear from the matrix elements?)

 

Cheers,

Jonathan

[elfmotat]

They're called "seagull graphs." See, for example, section 6.5.1 in David Tong's lecture notes: http://www.damtp.cam.ac.uk/user/tong/qft/six.pdf .

[JonathanApps]

So they do exist. Thanks! DAMTP just down the road from me....

[elfmotat]

No problem. By the way, the site will render your LaTeX for you if you wrap it in [*math][*/math] tags (without the *s).

[imatfaal]

The hijack - which was entirely my fault - has been split to here

 

http://www.scienceforums.net/topic/86107-latex-questions/#entry832149