1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Feynman rules in momentum space?

  1. Dec 3, 2011 #1
    I'm trying to do the following problem:

    ie. I'm trying to use the Feynman rules for momentum space to write down the mathematical expression that the diagram is supposed to represent. However, I don't feel very confident in what I've managed so far.

    Now as I understand it, these diagrams represent expressions that are equal to n-point Green's functions, where n is the number of external lines. So, looking at that diagram, I would think that the 2 straight lines coming off that single vertex are the external lines, so n=2.

    So, according to the Feynman rules, I assign them each a momentum pk each one gets a factor of [itex]\frac{i}{p_k^2 - m^2 +iε}[/itex].

    Also, another of the rules states that each internal line (which I take it means that single loop here) has a momentum kj and contributes a factor of [itex]∫\frac{d^4k_j}{2\pi^4}\frac{i}{k_j^2 - m^2 +iε}[/itex], and the vertex (the dot, right?) contributes a factor [itex] \frac{-iλ}{4!}2\pi\delta(\sum momenta)[/itex]. This gives:

    [tex]G_2(p_1,p_2) = \frac{i}{p_1^2 - m^2 +iε}\frac{i}{p_2^2 - m^2 +iε}∫\frac{d^4k}{2\pi^4}\frac{i}{k^2 - m^2 +iε}\frac{-iλ}{4!}2\pi\delta(p1+p2) = -\frac{\lambda}{4!}\frac{\delta(p_1 + p_2)}{(p_1^2 - m^2 +iε)(p_2^2 - m^2 +iε)}∫\frac{d^4k}{k^2 - m^2 +iε} [/tex]
    [tex] = -\frac{\lambda}{4!}\frac{1}{(p_1^2 - m^2 +iε)^2}∫\frac{d^4k}{k^2 - m^2 +iε}[/tex] since for the delta function to be equal to 1, we need p2 = -p1 (which ensures momentum is conserved at each vertex).

    Now this looks OK to me so far, but apparently I am supposed to also multiply this by a "combinatorial factor", which I have heard is supposedly 12, but I do not know how to get this, or what its significance is.
    Am I on the right lines here or what?

    Also, if anyone knows any good resources on the net (or elsewhere) that could help me understand this stuff better, I would appreciate it - the notes I'm learning from aren't the greatest. Ideally I could do with seeing some example problems with solutions, if you happen to know where any might be found.

  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted