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Annales Henri Poincaré

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

The Scaling and Mass Expansion

  • Michael Dütsch
Article

Abstract

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.

Keywords

Direct Extension Star Product Mass Expansion Renormalization Condition Commun Math Phys 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2014

Authors and Affiliations

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

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