I am a beginner in QFT, and my question is probably very basic.

As far as I understand, usually in QFT, in particular in QED, one postulates existence of IN and OUT states. Unitarity of the S-matrix is also essentially postulated. On the other hand, in more classical and better understood non-relativistic scattering theory unitarity of S-matrix is a non-trivial theorem which is proved under some assumptions on the
scattering potential, which are not satisfied automatically in general.
For example, unitarity of the S-matrix may be violated if the potential is too strongly attractive at small distances:
in that case a particle (or two interacting with each other particles) may approach each other from infinity and form a bound state.
(However the Coulomb potential is not enough attractive for this phenomenon.)

**The first question is why this cannot happen in the relativistic situation, say in QED.
Why electron and positron (or better anti-muon) cannot approach each other from infinity and form a bound state?**

As far as I understand, this would contradict the unitarity of S-matrix.
On the other hand, in principle S-matrix can be computed, using Feynmann rules, to any order of approximation in the coupling constants. Thus in principle unitarity of S-matrix could be probably checked in this sense to any order.

**The second question is whether such a proof, for QED or any other theory, was done anywhere? Is it written somewhere?**

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