Exploring Bound State Calculations in Quantum Field Theory

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Discussion Overview

The discussion centers on the search for comprehensive resources regarding bound state calculations in Quantum Field Theory (QFT). Participants express interest in both formalism and modern treatments beyond traditional texts, particularly in relation to the relativistic aspects of bound states.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant requests recommendations for review articles or books specifically focused on bound state calculations in QFT, noting a lack of extensive resources beyond brief mentions in textbooks.
  • Another participant provides a link to the original Bethe and Salpeter article on relativistic equations for bound state problems, mentioning additional related works, including a calculation by Bryce DeWitt.
  • A participant acknowledges knowledge of the Bethe-Salpeter paper and the Lapage-Brodsky equation but expresses a desire for more contemporary research on bound states in QFT.
  • One participant suggests that there may be relevant discussions in Weinberg's work, although they are uncertain about the completeness of the information.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the availability of modern resources for bound state calculations in QFT, with some expressing familiarity with older works while others seek more recent developments.

Contextual Notes

Participants indicate that existing literature may be limited to older papers and express uncertainty about the completeness of certain references. There is also a suggestion that relevant discussions might be found in less prominent journals or specific book chapters.

fermi
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Can anybody recommend a good review article (or a book) for bound state calculations in QFT? I have never seen anything along these lines, other than brief sections or paragraphs in various textbooks about the connection to the Schrödinger equation in the non-relativistic limit for two particle systems. Even if the fully relativistic treatment is difficult (or even impossible) to carry out numerical calculations with, I would like to see at least a well developed formalism that sets up the problem and analyzes it in great detail.
 
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http://cos.cumt.edu.cn/jpkc/dxwl/zl/zl1/Physical%20Review%20Classics/atomic/054.pdf
This links to the original article by Bethe and Salpeter "Relativistic equation for bound state problems". There was an article in the same issue of PR "Wave functions in momentum space" by Bethe & Salpeter but I dont't think it is online (for free anyway). There is also an interesting calculation summing the BS amplitudes of two scalar particles exchanging gravitons by Bryce DeWitt in Physical Review Letters Volume 13, Number 3 page 114, 20 July 1964.

Skippy
 
Last edited by a moderator:
skippy1729 said:
http://cos.cumt.edu.cn/jpkc/dxwl/zl/zl1/Physical%20Review%20Classics/atomic/054.pdf
This links to the original article by Bethe and Salpeter "Relativistic equation for bound state problems". There was an article in the same issue of PR "Wave functions in momentum space" by Bethe & Salpeter but I dont't think it is online (for free anyway). There is also an interesting calculation summing the BS amplitudes of two scalar particles exchanging gravitons by Bryce DeWitt in Physical Review Letters Volume 13, Number 3 page 114, 20 July 1964.

Skippy

Yes, I know about the well known Bethe-Salpeter paper. I am looking for something more modern, a treatment within QFT, rather than a relativistic two particle wave equation. I also know about the Lapage-Brodsky equation. But, one would think that there must be more work on bound states than just these forty year old papers. By the way, I did not know about DeWitt's work, I will check it out, thank you.

I am still hoping for a hidden review article somewhere, probably in a relatively obscure journal, or a good chapter or two in a book.
 
Last edited by a moderator:
I believe there is a discussion in Weinberg vol 1, but I haven't looked at it lately and don't recall how complete it is ...
 

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