Annales Henri Poincaré

, Volume 16, Issue 1, pp 163–188 | Cite as

The Scaling and Mass Expansion

  • Michael DütschEmail author


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 (Brunetti et al. in Commun Math Phys 208:623–661, 2000, Epstein et al. in Ann Inst Henri Poincaré 19A:211–295, 1973). 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(−(m 2(x 2ix 0 0))-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.


Direct Extension Star Product Mass Expansion Renormalization Condition Commun Math Phys 
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© Springer Basel 2014

Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany

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