Abstract
The relation between cutoff (lattice) field theory and renormalized field theory is investigated in detail for the ${({\ensuremath{\varphi}}^{4})}_{d}$ model by means of summed-up perturbation expansions. We show that the renormalized theory may be constructed as a large cutoff preasymptote of the bare theory avoiding completely subtractions for superficially divergent diagrams and cutoff limits. We stress the potential importance of this observation for the construction of strictly renormalizable field theories beyond perturbation theory. We analyze in detail the fundamental difference between superrenormalizable and strictly renormalizable models and its drawback to the possibility of constructing them as infinite cutoff limits.
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