Abstract
Mathematical construction of quantum field theory is reviewed with emphasis on the conceptual structure of the construction and on the role of rigorous renormalization group analysis without technical details. After explaining a rigorous formulation of a renormalization group method in a weak coupling region, a new approach in a strong coupling region is proposed in the context of the hierarchical approximation. An idea of proving triviality in d≥4 dimensions utilizing this new proposal concludes this review.
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