Why don't you say that the best exposition is in your [meomepuk = Eugene Stefanovich] 3 volume treatise on quantum electrodynamics ? I think this is a valid statement. Your treatise shows both the potential and the limitations of the dressed particle approach.There are many works in dressed/clothed particle theory. They usually pay tribute to the seminal paper
O. W. Greenberg, S. S. Schweber, "Clothed particle operators in simple models of quantum field theory", Nuovo Cim. 8 (1958), 378.
You can use Google Scholar to find all citations of this work. Currently this search shows 113 results.
It uses perturbatively constructible (but rigorously ill-defined) ''unitary'' transformations to renormalize standard perturbative QED. It misses, like any purely perturbative treatment of QFT, the infrared aspects of the theory. The faults show up in your version by predicting small superluminal effects.
No. You didn't prove the existence of the boost operator in your version of QED; you only give a perturbative construction for it, without showing its convergence. The superluminal effects you inherit are proof of the lack of true Lorentz invariance.4. This Hamiltonian is relativistically covariant: there exists a corresponding interacting boost operator such that all commutators of the Poincare Lie algebra are satisfied.
The devil is in the details, and getting the details right (as Glimm and Jaffe did in 2D) requires abandoning the Fock structure.