Axioms for renormalization in Euclidean quantum field theory (Q1063839)

A renormalization is formulated by \textit{K. Hepp} [Statistical mechanics and field theory, ed. \textit{C. de Witt, R. Stora} (1971; Zbl 0242.46002)] as a map which assigns to unrenormalized Feynman amplitudes the corresponding tempered distribution (called renormalized Feynman amplitude) in such a way that a set of axioms including Lorentz covariance, unitarity and causality are satisfied. The authors introduce a set of axioms for Euclidean renormalization which fixes it up to a finite renormalization and proves a one-to-one correspondence between Euclidean renormalizations formulated by the authors and the Minkowski space-time renormalization introduced by Hepp. The Euclidean counterpart of the analytic renormalization is shown to satisfy the axioms of the authors.