Why is the sum over all connected diagrams with a single source in QFT zero?

[PJK]

hi all,

i have a question regarding page 81 in Srednicki's QFT book. He states there that the sum over all connected diagrams with a single source is zero. Then he says that if you replace this single source by an arbitrary subdiagram the sum will still be zero. Can somebody explain why this is true?

 

[Avodyne]

The expression corresponding to the sum over all connected diagrams with a single source takes the form

\int d^4x\sum_i D_i(x)J(x),[/itex]<br /> <br /> where D_i(x) is everything in diagram i except the source (and will in general include integrals over other coordinates labeling other points in the diagram). The value of Y is adjusted to make this expression zero for <u>any</u> function J(x); that is, so that \sum_i D_i(x)=0. So, we can replace J(x) with any other expression, including something corresponding to some other arbitrary subdiagram.

 

[PJK]

Thank you very much! Sometimes I wished Srednicki would include one or two more sentences in his argumentation...

 

[malawi_glenn]

Thank you very much! Sometimes I wished Srednicki would include one or two more sentences in his argumentation...

me too, I have wrote down many things that I would like to give to him as suggestion for a 2nd edition :-)

 

[RedX]

I thought the 2nd edition of Srednicki was already out or about to be? I offered a few corrections and I think he said it was too late for the 2nd edition (or maybe he didn't say that and I just remember seeing that he changed the errata on his website and deleted all the corrections to the 1st edition).

I find Srednicki's book to be very good but there are some parts where you can feel he didn't feel like explaining something. Like how can you just integrate out a heavy field by substituting its classical solution back into the Lagrangian? For some reason you can ignore the source term (the current times the field) when you do this. But overall I think it's nice.

 

[malawi_glenn]

I know, it is like sometimes he explains that -(-1) = 1 but never the readl hard issues which has to do with QFT to do.

Maybe he meant the second PRINTING, I have the 3rd printing of the 1st edition.

 

[haushofer]

I also have the feeling that in a lot of aspects Srednicki is very good, but there are still some explanations lacking. I'm now reading the book quite thoroughly, and some things are still not completely clear to me. I'm thinking about putting some things which were mystifying for me and which I nevertheless managed to find out after quite some work (like Malawi Glenn's question about exercise 2.2) in a TeX-file as some sort of supplement. Ofcourse, some hard work to get results isn't wrong, but if things are represented as easy and turn out to be hard, then it can be very time consuming. :)