Exploring Bound State Calculations in Quantum Field Theory

In summary, there is a lot of work on bound state calculations, but it seems to be more developed for quantum field theory than for QFT.
  • #1
fermi
76
5
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 Schrodinger 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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  • #2
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
 
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  • #3
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.
 
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  • #4
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 ...
 

1. What is the bound state formalism in QFT?

The bound state formalism in QFT (quantum field theory) is a mathematical framework used to describe the behavior of particles that are bound together by a force, such as atoms and nuclei. It is a non-perturbative approach that takes into account the interactions between the particles and their surrounding fields.

2. How is the bound state formalism different from other approaches in QFT?

The bound state formalism is different from other approaches in QFT, such as perturbation theory, because it takes into account the strong interactions between particles that cannot be described by perturbation methods. It also allows for the calculation of bound state properties, such as mass and energy, which are not accessible through perturbative methods.

3. What are some applications of the bound state formalism in QFT?

The bound state formalism in QFT has many applications in particle physics, nuclear physics, and condensed matter physics. It is used to study the properties of bound states, such as the binding energy and decay rates, and to understand the behavior of strongly interacting systems.

4. How does the bound state formalism relate to the concept of confinement in QCD?

The bound state formalism is closely related to the concept of confinement in QCD (quantum chromodynamics), which describes the strong interactions between quarks and gluons. Confinement refers to the phenomenon where quarks and gluons are confined within hadrons, such as protons and neutrons, and cannot exist as free particles. The bound state formalism provides a way to understand and calculate the properties of these hadrons.

5. Are there any limitations to the bound state formalism in QFT?

Although the bound state formalism is a powerful tool for studying bound states, it does have some limitations. It is difficult to apply to systems with a large number of particles or to systems with extremely high energies. It also does not take into account effects of quantum gravity, so it cannot be used to study phenomena on a very small scale or at very high energies.

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