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- 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.

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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