Srednicki 9.17, 9.18: Sum of Diagrams with Single Source Removed

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Discussion Overview

The discussion centers around the interpretation of expression 9.17 from Srednicki's work, specifically regarding the sum of diagrams with a single source removed. Participants explore the relationship between diagrams and terms in the double Taylor expansion of Z_1(J).

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions why expression 9.17 represents the sum of all diagrams with a single source removed, suggesting a connection to the double Taylor expansion of Z_1(J).
  • Another participant explains that the expression involves taking a derivative with respect to J, which removes one factor of J and sets all other factors to zero, leading to the conclusion that only diagrams with a single J survive.
  • A third participant expresses gratitude for the explanation and reflects on their own understanding of the material.
  • One participant shares their familiarity with Srednicki's work, attributing their expertise to earlier drafts of related material they found superior to existing textbooks.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of expression 9.17, as one participant questions the reasoning while another provides an explanation. The discussion remains open with differing perspectives on the topic.

Contextual Notes

There may be missing assumptions regarding the definitions of terms and the specific context of the diagrams discussed, which could affect the interpretation of expression 9.17.

kexue
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Why is the expression 9.17 the sum of all diagrams with a single source removed?

I thought diagrams stand for terms in double taylor expansion of Z_1(J).
 
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The expression in 9.17 is

[tex]{\delta\over\delta J(x)}Z_1(J)\Bigr|_{J=0}[/tex]

The derivative with respect to J removes one factor of J, and then all other factors of J are set to zero. So the only surviving diagrams are those that had just one J to begin with.
 
Thanks, Avodyne!

Actually, when I stared at it again this morning, I already figured it out by myself.

How come your such an expert on Srednick's book? Always when someone ask a question to his book, you give the answer right away. I remember you gave me great answers like one year back ago, which i have written as side notes in the book.
 
kexue said:
How come your such an expert on Srednick's book? Always when someone ask a question to his book, you give the answer right away. I remember you gave me great answers like one year back ago, which i have written as side notes in the book.
Srednicki had posted rough drafts of Spin Zero and Spin One Half at arxiv.org in 2004, and I thought they were much better than the existing textbooks, so by now I know the material pretty well.
 

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