Exploring Bound State Calculations in Quantum Field Theory

[fermi]

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.

 

[skippy1729]

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

 

[fermi]

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.

 

[Avodyne]

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 ...