Regarding Coleman's Sine-Gordon Duality

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Discussion Overview

The discussion revolves around Coleman's Sine-Gordon duality, specifically focusing on the calculations presented in his paper, particularly equation 4.11. Participants are examining the nature of the time-ordered correlation function and its implications in quantum field theory (QFT).

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Homework-related

Main Points Raised

  • One participant questions the meaning of the expression $$\mathcal{T} \langle 0 | \prod_i A_+ (x_i) A_-(y_i) | 0 \rangle$$ and seeks clarification on why the operators ## A_+ (x_i) ## and ## A_-(y_i) ## are not at the same point.
  • Another participant identifies the expression as a time-ordered correlation function but does not elaborate on its physical significance.
  • A third participant acknowledges the time-ordered nature of the correlation function but expresses confusion regarding the specific perturbation series being calculated and its physical meaning.
  • One participant reiterates the need for a foundational understanding of QFT before delving into the paper's content.

Areas of Agreement / Disagreement

There is no consensus on the specific physical meaning of the perturbation series being calculated, and participants express varying levels of understanding regarding the foundational concepts of QFT.

Contextual Notes

Some participants suggest that a basic understanding of QFT is necessary to fully grasp the calculations in the paper, indicating potential limitations in the discussion due to varying levels of expertise among participants.

QFT1995
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TL;DR
Confusion over perturbative series
The link to the paper is here; http://www.sbfisica.org.br/~evjaspc/xviii/images/Nunez/Jan26/AdditionalMaterial/Coleman_paper/Coleman_paper.pdf

Im confused over what exactly he is calculating on page 5 (2092) equation 4.11. Specifically what is
$$\mathcal{T} \langle 0 | \prod_i A_+ (x_i) A_-(y_i) | 0 \rangle. $$
Why aren't the ## A_+ (x_i) ## and ##A_-(y_i)## at the same point and what exactly is the object above?
 
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It's a time ordered correlation function. Before studying this paper, you should first learn some more basic QFT (if you haven't already).
 
I understand that its a time ordered correlation function but I'm confused on exactly what the specific perturbation series he is calculating physically means.
 
It's a time ordered correlation function. Before studying this paper, you should first learn some more basic QFT (if you haven't already).

Hi, could you help explain the specific series in the paper. I'm on a deadline and I don't have much time.
Thanks
 

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