The scaling and mass expansion
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Submission date: 14. Jan. 2014
published in: Annales Henri Poincaré, 16 (2015) 1, p. 163-188
DOI number (of the published article): 10.1007/s00023-014-0324-6
Keywords and phrases: Perturbative quantum field theory, Causal perturbation theory
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The scaling and mass expansion (shortly ’sm-expansion’) is a new axiom for causal perturbation theory, which is a stronger version of a frequently used renormalization condition in terms of Steinmann’s scaling degree. If one quantizes the underlying free theory by using a Hadamard function (which is smooth in m ≥ 0), one can reduce renormalization of a massive model to the extension of a minimal set of mass-independent, almost homogeneously scaling distributions by a Taylor expansion in the mass m. The sm-expansion is a generalization of this Taylor expansion, which yields this crucial simpliﬁcation of the renormalization of massive models also for the case that one quantizes with the Wightman two-point function, which contains a log(−(m2(x2−ix00))-term. We construct the general solution of the new system of axioms (i.e. the usual axioms of causal perturbation theory completed by the sm-expansion), and illustrate the method for a divergent diagram which contains a divergent subdiagram.