Explaining Equation (2.8) from Equation (2.6)

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Discussion Overview

The discussion revolves around the derivation of equation (2.8) from equation (2.6) as presented in lecture notes. Participants are exploring the relationships between these equations and referencing additional materials for clarification.

Discussion Character

  • Technical explanation
  • Homework-related
  • Debate/contested

Main Points Raised

  • One participant requests clarification on how equation (2.8) follows from equation (2.6) in the provided lecture notes.
  • Another participant suggests that equation (2.8) is derived from (2.6) using equation (2.9), which itself is derived from (2.10), indicating a need to read the equations in reverse order.
  • A participant expresses gratitude and attempts to summarize the expansion of Z[J(y)], questioning the absence of integrals in a similar expansion found in a book by Tony Zee.
  • One participant claims there is a typo in Zee's work, stating that integrals were omitted in the first edition but included in the second edition.
  • The original poster seeks further hints on inserting equation (2.6) into (2.8) to confirm their understanding of the expansion of Z[J(y)].

Areas of Agreement / Disagreement

Participants express varying interpretations of the equations and their derivations, with some suggesting corrections to published materials. The discussion remains unresolved regarding the exact nature of the derivation and the presence of typos.

Contextual Notes

There are references to specific equations and potential typos in published materials, which may affect the clarity of the discussion. The participants' understanding relies on the context provided in the lecture notes and external references.

Lapidus
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Could someone explain to me how equation (2.8) follows from equation (2.6) on page 20 (pdf page 21) http://www.physics.utoronto.ca/~luke/PHY2403/References_files/lecturenotesII.pdf"

It must be easy.

thanks!
 
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He derives (2.8) from (2.6) by using (2.9)! Which in turn follows from (2.10). You just have to read it backwards...
 
Many thanks, Bill_K!

So do I get Z[J(y)]= 1 + Z[J(x_1)] +(1/2)Z[J(x_1)]Z[J(x_2)] + (1/3)Z[J(x_1)]Z[J(x_2)]Z[J(x_3)] + ... ? Does that make sense?

Tony Zee expands Z(J) in his book, too, http://press.princeton.edu/chapters/s9227.pdf" first line of equation (13). But why does he not have the integrals over x in his expansion? Has that something to do with the Z(0,0) in front?

again, thank you
 
Last edited by a moderator:
It's a typo!

Zee forgot to put the integrals in the equation. I checked, in the second edition they are there.

But back to my initial problem in the lecture notes from Michael Luke. When I insert 2.6 into 2.8 do I get Z[J(y)]= 1 + Z[J(x_1)] +(1/2)Z[J(x_1)]Z[J(x_2)]+(1/3)Z[J(x_1)]Z[J(x_2)]Z[J(x_3)] + ... ?

I would welcome any further hints. thank you
 

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