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Dimension of n-point Green function

  1. Feb 23, 2014 #1
    Hi everyone. I have a very quick question. Can someone tell me how to compute the energy dimensions of an n-point Green function. Consider for example a [itex]\lambda\phi^4[/itex] scalar theory. I know that the dimensions of an n-pt Green function are [itex]4-n[/itex] (or something like that). How do I prove it?

  2. jcsd
  3. Feb 23, 2014 #2
    The dimension of anything in QFT theory can be calculated by counting factors. Each field derivative or integral contributes to the overall dimension.
  4. Feb 24, 2014 #3
    Yes, I know that. For example in a scalar theory the dimension of the fields is 1 (in energy). My question is: how do I go from knowing the dimension of the field to knowing the dimension of the Green function?
  5. Feb 26, 2014 #4
    If you are working in D=2d dimensions,then n-point connected 1PI Green function reads
    Gn(p1,p2,....,pn)=∫∏i=1to nd2dxiei(p1x1+....pnxn)<0|[itex]T\phi(x_1)....\phi(x_n)[/itex]|0>.
    dim. of [itex]\phi[/itex] is d-1 here as you can check,and dim. of d2dx is -2d because length dimension is inverse of energy(mass) dimension.Hence Gn has dimension n(d-1)-2nd=-n(d+1)

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