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Dimension of npoint Green function 
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#1
Feb2314, 05:35 PM

P: 321

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


#2
Feb2314, 11:57 PM

Thanks
P: 1,948

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



#3
Feb2414, 07:31 AM

P: 321

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
Feb2614, 05:42 AM

P: 1,020

Dimension of npoint Green function
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 d1 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(d1)2nd=n(d+1) 


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