QFT Field Expansion: Explaining (2.72) - Schwartz

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Discussion Overview

The discussion centers around understanding a specific equality in equation (2.72) from Schwartz's work on quantum field theory (QFT). Participants are attempting to clarify how to incorporate previous equations (2.69) and (2.71) into this context.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • Some participants seek clarification on the second equality sign in (2.72) and how it relates to equations (2.69) and (2.71).
  • One participant expresses difficulty in incorporating (2.69) into their understanding of (2.72) and asks for ideas.
  • Another participant suggests rewriting (2.69) to show the commutation relation and proposes expanding the left side to use it in (2.72).
  • A later reply reiterates the suggestion to rewrite (2.69) and expand the left side, indicating a potential approach to the problem.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the explanation of (2.72), as there are varying levels of understanding and approaches suggested regarding the use of (2.69) and (2.71).

Contextual Notes

Some participants may be missing assumptions or specific steps in the mathematical reasoning required to fully understand the transition from (2.69) to (2.72). The discussion does not resolve these potential gaps.

John Fennie
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The attached pic is from Schwartz.
Can someone explain the second equality sign in (2.72)?
 

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John Fennie said:
The attached pic is from Schwartz.
Can someone explain the second equality sign in (2.72)?

Use (2.69) and (2.71).
 
George Jones said:
Use (2.69) and (2.71).
Hi that is my problem. I wasn't able to incorporate (2.69). Is there an idea?
 
Rewrite (2.69) as
$$\left[ a_p , a_k^\dagger \right] = \left(2\pi\right)^3 \delta \left( \vec k - \vec p \right),$$
expand the left side, and use this in (2.72).
 
George Jones said:
Rewrite (2.69) as
$$\left[ a_p , a_k^\dagger \right] = \left(2\pi\right)^3 \delta \left( \vec k - \vec p \right),$$
expand the left side, and use this in (2.72).
Thank you!
 

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