Dimension of n-point Green function

[Einj]

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

 

[dauto]

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

 

[Einj]

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?

 

[andrien]

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?

If you are working in D=2d dimensions,then n-point connected 1PI Green function reads
G_n(p₁,p₂,...,p_n)=∫∏_{i=1to n}d^2dx_ie^{i(p₁x₁+...p_nx_n)}<0|$T\phi(x_1)...\phi(x_n)$|0>.
dim. of $\phi$ is d-1 here as you can check,and dim. of d^2dx is -2d because length dimension is inverse of energy(mass) dimension.Hence Gⁿ has dimension n(d-1)-2nd=-n(d+1)