# The scaling and mass expansion

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: http://inspirehep.net/info/faq/general#utf8
%%% 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;%%"
}

Keywords:

*none*