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
The dimension of anything in QFT theory can be calculated by counting factors. Each field derivative or integral contributes to the overall dimension.
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}(p_{1},p_{2},....,p_{n})=∫∏_{i=1to n}d^{2d}x_{i}e^{i(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 d^{2d}x is -2d because length dimension is inverse of energy(mass) dimension.Hence G^{n} has dimension n(d-1)-2nd=-n(d+1)