What is the origin of QFT "difficulties": "physical" or "mathematical"?

Question

Indeed, there is a 'currently" dominating "opinion" that relativistic QFT is "dictated" by this and that, so it is unavoidable that we encounter UV and IR difficulties. This and that are considered as ultimately established things amongst which there are Poincaré invariance, locality, etc., etc.

And in my opinion, there is still a room of improving the QFT initial states and interactions so that no UV and IR difficulties may appear. I propose you to express your opinion whether the current QFT is (are) satisfactory. Especially it concerns "gauge" interactions.

My question is motivated with mathematical approaches to QFTs like algebraic, axiomatic, etc. approaches. As to me, I think we have already sufficient experience in obtaining the final QFT results that may help us construct a theory without "difficulties".

Comments

Poincare invariance is what defines relativistic physics in general, whether classical or quantum. It is not just an opinion but a demarcation criterion.

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You prove nothing at all in the relativistic context since your toy theories don't respect Lorentz invariance. Whereas the consensus of the physicists (embodied in the standard model) is corroborated by a huge number of experiments. 

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Your main methodological error is that you dismiss the fact that the (Lorentz invariant) standard model passes almost all experimental tests with flying colors while your proposed alternative is nothing but a sketch of a hope, and doesn't accommodate Lorentz invariance, the most important requirement for a relativistic theory.

You also mistake the (free QFT) scaffolding for the (renormalized) final theory. It is like mistaking the power functions for the exponential function, since the latter can be defined as a power series.

The standard model is strongly coupled, due to renormalization and the summing of contributions from infinitely many Feynman diagrams, resulting, e.g., in poles in S-matrix elements indicating bound states. The latter are proof that strong coupling exists and is accounted for,.

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The missing care consists of talking about big projects and proposals without first making sure that there is a basis for it. It is known for a long time that once one tries to get the Lorentz generators behave correctly, all problems show up that you are currently avoiding to tackle. They are not solvable by simply accounting for photon clouds but only by taking into account all what is already known, including the renormalization stuff.

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The only error made in the naive discussion is to assume that the asymptotic states are given by plane waves, which is incompatible with massless fields. You simply take the naive version for the one physicists use when making real predictions, and hence you find ''errors'' that you (unlike Kulish and Faddev) don't cure but only play with using your toys. 

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<p>I don't care what you blame. The analysis of Kulish and Faddeev (and lots of other work) shows that the initial and final states must be coherent states, not plane waves. Once this is accounted for, the S-matrix elements exist, and what you consider a grave error disappears.&nbsp;</p>

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No, you don't care, that's right. And my independent analysis and original construction ("electronium") show too that the finals states are quasi-coherent ones for soft photons. As well, as the "electronium" is a soft compound system, it is unlikely to prepare it in its "ground" state, i.e., again quasi-coherent states in the initial state. You completely missed this result in my approach. You spread lies about my approach and about me personally.