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3

It's not a sufficient explanation. There are asymptotically free theories which are not strongly coupled in the IR. The rate at which the coupling gets strong is important. In QCD, it seems to get strong very quickly near the confinement scale, so that beyond a certain scale, you only see hadrons. It is not really understood how this works. The ...

2

In principle one has to calculate the pole of correlation functions involving gauge invariant operators like $\text{Tr}F_{\mu\nu}F^{\mu\nu}$. The problem is that due to asymptotic freedom, QCD is not solvable perturbatively at low energies. This is why nonperturbative techniques like lattice QCD are used to calculate such spectra. A key achievement in this ...

2

I) Vanishing field-strength $F=0$ does not imply that the gauge potential $A$ is pure gauge. It only holds locally. There could be global obstructions. In fact, topological obstructions could happen even if the gauge group $G$ is Abelian. II) Let us sketched the proof of the local statement in a sufficiently small neighborhood $\Omega\subseteq M$ of a point ...

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