Deriving Srednicki eqn. (9.19)

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Discussion Overview

The discussion focuses on deriving equation (9.19) from Srednicki's Quantum Field Theory (QFT) book, specifically within the context of \(\phi^3\) theory and its differences from \(\phi^4\) theory. Participants explore the necessary steps and concepts involved in this derivation.

Discussion Character

  • Technical explanation, Debate/contested, Homework-related

Main Points Raised

  • One participant requests assistance in deriving equation (9.19) from Srednicki's book.
  • Another participant emphasizes the importance of following homework forum guidelines when asking for help.
  • A participant clarifies that the problem is not a homework issue and notes the differences in diagrammatic representation between \(\phi^3\) and \(\phi^4\) theories, which complicates consulting other resources.
  • Another participant explains that equation (9.19) is derived from the sum of specific diagrams in Srednicki's figures and mentions the need to introduce a counterterm in the Lagrangian, which is not required in \(\phi^4\) theory.
  • This participant also describes the modifications needed in the derivation process, including changes to the integral and coefficients, and suggests expanding as Srednicki does in a related equation.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the problem, with some considering it a homework question while others assert it is not. The discussion remains unresolved regarding the specific steps and modifications needed for the derivation.

Contextual Notes

Participants note that the introduction of a counterterm and its implications for the derivation process may not be straightforward, particularly due to the differences between \(\phi^3\) and \(\phi^4\) theories. There are also references to specific equations and figures that may require further clarification.

omephy
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can anybody help me to derive eqn. (9.19) of Srednicki's QFT book?
 
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omephy said:
can anybody help me to derive eqn. (9.19) of Srednicki's QFT book?
Yes -- but to be polite, you should adhere to the guidelines of the homework forums when asking questions like this.
 
It is not a homework problem. Srednicki uses \phi^3 theory and therefore its diagrammatic representation is quite different from the books written in \phi^4 theory. so, I can't even consult other books to derive that equation or to understand the underlying concept. So, I have asked for help.
 
So 9.19 is the sum of the first diagram in Figure 9.12 and Figure 9.3. Now if you want to derive the diagrams in Figure 9.12 from scratch you need to introduce the counterterm (This isn't necessary in \phi^4, so maybe this is where the confusion lies) in the Lagrangian. When you do this you have to rewrite 9.10 to include another exponential (due to the counterterm) which will have (\frac{1}{i}\frac{\delta}{\delta J(x)}) in the integral. You'll also have to change the coefficients in front of the integral in the exponential. Then you can expand like Srednicki does in 9.11, but now you'll have three sums instead of two.
 

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