# QED Bound States: Weinberg's Explanation & Breakdown

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• Jamister
In summary, Weinberg discusses the problematic nature of bound states in QED due to perturbation theory breaking down. He uses the example of the hydrogen atom to explain this concept, discussing time-ordered diagrams and the factor [q^2/m_e]^-1. While Weinberg claims that the momentum space integration is q^3, there is debate over its contribution. Despite technical questions, it is clear that perturbation theory breaks down, even though QM shows that the hydrogen atom has a perfect ground state due to the Coulomb interaction, a result of QED. Weinberg's book further delves into the use of perturbation theory and the Coulomb gauge to understand the hydrogen spectrum. The bound state energies can be determined by
Jamister
TL;DR Summary
bound states are problematic in QED and QFT in general.
Weinberg writes in his book on QFT Vol1 that bound states in QED are problematic because perturbation theory breaks down. consider the case of hydrogen atom, electron+proton. Weinberg explains this case and I copy from the book:

https://www.physicsforums.com/attachments/247655
what is time ordered diagrams of old fashion perturbation theory?
I don't understand his explanation. What is this factor ## [q^2/ m_e]^{-1} ## ?
In Addition,Weinberg claims the momentum space integration is ##q^3## but I think it is necessary to the integral to know its contribution.
but aside those technical question, how is that perturbation theory breaks down, while we know from QM that for a coulomb interaction we have a perfect ground state for the hydrogen atom, and the coulomb interaction is a direct result of QED.

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Well, just read on in Weinberg's book.

To get the hydrogen spectrum you start perturbation theory from another split of the Hamiltonian into ##H_0## and ##H_I##, using the Coulomb gauge, which is more convenient than the covariant gauges in this case.

You can also see this from usual Feynman diagrams. The bound state energies of a proton and an electron is formally given by the poles of the the scattering amplitude for ep->ep. To get poles you have to resum an infinite number of diagrams (at least "ladder diagrams"). This approach is nicely discussed in Landau&Lifshitz, vol. 4.

Jamister

## 1. What is QED Bound States?

QED Bound States, also known as Quantum Electrodynamics Bound States, are a type of particle that is bound together by the electromagnetic force. These particles are made up of a charged particle and its corresponding antiparticle, and they are held together by the exchange of virtual photons.

## 2. Who first explained QED Bound States?

The explanation of QED Bound States was first provided by physicist Steven Weinberg in 1965. His explanation was based on the principles of quantum field theory and the concept of virtual particles.

## 3. How does Weinberg's explanation of QED Bound States work?

Weinberg's explanation of QED Bound States involves the exchange of virtual photons between a charged particle and its antiparticle. These virtual photons create a force that binds the particles together, similar to how real photons create the electromagnetic force between charged particles.

## 4. What is the breakdown of QED Bound States?

The breakdown of QED Bound States occurs when the distance between the particles becomes too large for the virtual photons to maintain their binding force. This results in the particles becoming unbound and separating from each other.

## 5. What are some real-world applications of QED Bound States?

QED Bound States have been observed in experiments involving high-energy collisions, such as those at the Large Hadron Collider. They also play a role in the behavior of atoms and molecules, and are important in understanding the properties of materials and chemical reactions.

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