The scaling and mass expansion

Michael Dütsch
January 08, 2014
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 $m\geq 0$), 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 $\log(-(m^2(x^2-ix^0 0))$-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.
open access link Ann. Henri Poincare 16 (1), (2015), 163-188 article file
%%% contains utf-8, see: %%% add \usepackage[utf8]{inputenc} to your latex preamble @article{Duetsch:2014lfa, author = "Dütsch, Michael", title = "{The scaling and mass expansion}", journal = "Annales Henri Poincare", volume = "16", year = "2015", number = "1", pages = "163-188", doi = "10.1007/s00023-014-0324-6", eprint = "1401.1670", archivePrefix = "arXiv", primaryClass = "math-ph", SLACcitation = "%%CITATION = ARXIV:1401.1670;%%" }