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But usual renormalized perturbation theory leads to a unitary Poincare-covariant S-matrix, fulfilling the linked-cluster principle (order by order).
I always understood that the Epstein-Glaser approach as in Scharff's book is equivalent to the usual perturbation theory using standard counterterm subtraction, and it's also called "causal". It's also in a sense very physical since it "smears" the distribution valued field operators, introducing a scale, which is necessary to define QFT as an effective theory in the first place.
QED may or may not be plagued by a Landau pole, but as an effective theory at least up to the energies available today in experiments it's still among the most successful theories ever.
I always understood that the Epstein-Glaser approach as in Scharff's book is equivalent to the usual perturbation theory using standard counterterm subtraction, and it's also called "causal". It's also in a sense very physical since it "smears" the distribution valued field operators, introducing a scale, which is necessary to define QFT as an effective theory in the first place.
QED may or may not be plagued by a Landau pole, but as an effective theory at least up to the energies available today in experiments it's still among the most successful theories ever.