# Dimension of n-point Green function

1. ### Einj

444
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 $\lambda\phi^4$ scalar theory. I know that the dimensions of an n-pt Green function are $4-n$ (or something like that). How do I prove it?

Thanks

2. ### dauto

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

3. ### Einj

444
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?

4. ### andrien

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|$T\phi(x_1)....\phi(x_n)$|0>.
dim. of $\phi$ 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)