Dimension of n-point Green function

  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?

    Thanks
     
  2. jcsd
  3. The dimension of anything in QFT theory can be calculated by counting factors. Each field derivative or integral contributes to the overall dimension.
     
  4. 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. 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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